Dissertations / Theses on the topic 'Stochastic modelling'
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1
Ozkan, Erhun. "Stochastic Inventory Modelling." Master's thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/3/12612097/index.pdf.
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In this master thesis study, new inventory control mechanisms are developed for the
repairables in Nedtrain. There is a multi-item, multi echelon system with a continuous
review and one for one replenishment policy and there are different demand supply
options in each control mechanism. There is an aggregate mean waiting time constraint
in each local warehouse and the objective is to minimize the total system cost. The base
stock levels in each warehouse are determined with an approximation method. Then
different demand supply options are compared with each other.
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Baduraliya, Chaminda Hasitha. "Stochastic modelling in finance." Thesis, University of Strathclyde, 2012. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=16938.
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The trading of financial derivatives and products in financial markets has influenced the development of the world economy. Over the last few decades, a rapid growth in complex financial systems, which can generate unstable conditions in financial markets, has been observed. Therefore models are being developed to study and examine the uncertainty surrounding these financial systems in different circumstances. The important milestone of this work can be traced to the Black-Scholes formula for option pricing which was published in 1973 and revolutionized the financial industry by introducing the no-arbitrage principle [8]. This model assumed that the average rates of return and volatility are constant, however, this is not realistic. Therefore, several models have been developed, based on pragmatic studies, which generalize the Black-Scholes formula to acquire more knowledge for these financial systems. In this project, we will focus on Stochastic Differential Equations (SDEs) models in finance which do not have explicit solutions so far. In particular, Lewis [47] developed the mean-reverting-theta processes which can not only model the volatility but also the asset price. Therefore, we will establish the Euler-Maruyama (EM) numerical schemes to approximate the solution to this model and show that the EM approximate solution will converge in probability to the true solution under certain conditions. The convergence property of the corresponding step process will be examined under the same conditions to determine its application in finance. In addition, the Markov-switching format of this model can be used to explain some erratic situations observed in financial data. Under the same conditions on parameters of mean-reverting-theta model, the Markov-switching model will be examined to show that the EM approximate solution to this model will converge in probability to the true solution. Although previous models fit to a certain type of financial data, they can not be used to explain behaviour of the unpredictable abrupt structural changes in financial markets. However, the mean-reverting-theta stochastic volatility model driven by a Poisson jump process explains some of this phenomenon. Therefore, we will examine the analytical properties of EM approximate solutions to this model for two conditions of the parameters theta and beta. Since it is possible to obtain a more generalized formula for this stochastic volatility jump process, by incorporating a hybrid concept into this SDE model, we will consider the mean-reverting-theta volatility model with Poisson jumps driven by two independent Markov processes. Existing financial instruments are not strong enough to examine the convergence property of the approximate solution to this model. Therefore, we will establish EM approximate solutions to this model and examine their convergence property, when we assume similar parameter conditions to the mean-reverting-theta model. Finally, we will show that these approximate solutions of the SDE models can be used to evaluate financial quantities, options and bonds for example.
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Chen, Peng. "Modelling the Stochastic Correlation." Thesis, KTH, Matematisk statistik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-188501.
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In this thesis, we mainly study the correlation between stocks. The correlation between stocks has been receiving increasing attention. Usually the correlation is considered to be a constant, although it is observed to be varying over time. In this thesis, we study the properties of correlations between Wiener processes and introduce a stochastic correlation model. Following the calibration methods by Zetocha, we implement the calibration for a new set of market data.I det här examensarbetet fokuserar vi främst på att studera korrelation mellan aktier. Korrelationen mellan aktier har fått allt större uppmärksamhet. Vanligtvis antas korrelation vara konstant, trots att empiriska studier antyder att den är tidsvarierande. I det här examensarbetet studerar vi egenskaper hos korrelationen mellan Wienerprocesser och inför en stokastisk korrelationsmodell. Baserat på kalibreringsmetoder av Zetocha implementerar vi kalibrering för en ny uppsättning av marknadsdata.
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Lopes, Moreira de Veiga Maria Helena. "Modelling and forecasting stochastic volatility." Doctoral thesis, Universitat Autònoma de Barcelona, 2004. http://hdl.handle.net/10803/4046.
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El objetivo de esta tesis es modelar y predecir la volatilidad de las series financieras con modelos de volatilidad en tiempo discreto y continuo.En mi primer capítulo, intento modelar las principales características de las series financieras, como a persistencia y curtosis. Los modelos de volatilidad estocástica estimados son extensiones directas de los modelos de Gallant y Tauchen (2001), donde incluyo un elemento de retro-alimentación. Este elemento es de extrema importancia porque permite captar el hecho de que períodos de alta volatilidad están, en general, seguidos de periodos de gran volatilidad y viceversa. En este capítulo, como en toda la tesis, uso el método de estimación eficiente de momentos de Gallant y Tauchen (1996). De la estimación surgen dos modelos posibles de describir los datos, el modelo logarítmico con factor de volatilidad y retroalimentación y el modelo logarítmico con dos factores de volatilidad. Como no es posible elegir entre ellos basados en los tests efectuados en la fase de la estimación, tendremos que usar el método de reprogección para obtener mas herramientas de comparación. El modelo con un factor de volatilidad se comporta muy bien y es capaz de captar la "quiebra" de los mercados financieros de 1987.
En el segundo capítulo, hago la evaluación del modelo con dos factores de volatilidad en términos de predicción y comparo esa predicción con las obtenidas con los modelos GARCH y ARFIMA. La evaluación de la predicción para los tres modelos es hecha con la ayuda del R2 de las regresiones individuales de la volatilidad "realizada" en una constante y en las predicciones. Los resultados empíricos indican un mejor comportamiento del modelo en tiempo continuo. Es más, los modelos GARCH y ARFIMA parecen tener problemas en seguir la marcha de la volatilidad "realizada".
Finalmente, en el tercer capítulo hago una extensión del modelo de volatilidad estocástica de memoria larga de Harvey (2003). O sea, introduzco un factor de volatilidad de corto plazo. Este factor extra aumenta la curtosis y ayuda a captar la persistencia (que es captada con un proceso integrado fraccional, como en Harvey (1993)). Los resultados son probados y el modelo implementado empíricamente.
The purpose of my thesis is to model and forecast the volatility of the financial series of returns by using both continuous and discrete time stochastic volatility models.
In my first chapter I try to fit the main characteristics of the financial series of returns such as: volatility persistence, volatility clustering and fat tails of the distribution of the returns.The estimated logarithmic stochastic volatility models are direct extensions of the Gallant and Tauchen's (2001) by including the feedback feature. This feature is of extreme importance because it allows to capture the low variability of the volatility factor when the factor is itself low (volatility clustering) and it also captures the increase in volatility persistence that occurs when there is an apparent change in the pattern of volatility at the very end of the sample. In this chapter, as well as in all the thesis, I use Efficient Method of Moments of Gallant and Tauchen (1996) as an estimation method. From the estimation step, two models come out, the logarithmic model with one factor of volatility and feedback (L1F) and the logarithmic model with two factors of volatility (L2). Since it is not possible to choose between them based on the diagnostics computed at the estimation step, I use the reprojection step to obtain more tools for comparing models. The L1F is able to reproject volatility quite well without even missing the crash of 1987.
In the second chapter I fit the continuous time model with two factors of volatility of Gallant and Tauchen (2001) for the return of a Microsoft share. The aim of this chapter is to evaluate the volatility forecasting performance of the continuous time stochastic volatility model comparatively to the ones obtained with the traditional GARCH and ARFIMA models. In order to inquire into this, I estimate using the Efficient Method of Moments (EMM) of Gallant and Tauchen (1996) a continuous time stochastic volatility model for the logarithm of asset price and I filter the underlying volatility using the reprojection technique of Gallant and Tauchen (1998). Under the assumption that the model is correctly specified, I obtain a consistent estimator of the integrated volatility by fitting a continuous time stochastic volatility model to the data. The forecasting evaluation for the three estimated models is going to be done with the help of the R2 of the individual regressions of realized volatility on the volatility forecasts obtained from the estimated models. The empirical results indicate the better performance of the continuous time model in the out-of-sample periods compared to the ones of the traditional GARCH and ARFIMA models. Further, these two last models show difficulties in tracking the growth pattern of the realized volatility. This probably is due to the change of pattern in volatility in this last part of the sample.
Finally, in the third chapter I come back to the model specification and I extend the long memory stochastic volatility model of Harvey (1993) by introducing a short run volatility factor. This extra factor increases kurtosis and helps the model capturing volatility persistence (that it is captured by a fractionally integrated process as in Harvey (1993) ). Futhermore, considering some restrictions of the parameters it is possible to fit the empirical fact of small first order autocorrelation of squared returns. All these results are proved theoretically and the model is implemented empirically using the S&P 500 composite index returns. The empirical results show the superiority of the model in fitting the main empirical facts of the financial series of returns.
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Löfdahl, Björn. "Stochastic modelling in disability insurance." Licentiate thesis, KTH, Matematisk statistik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-134233.
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This thesis consists of two papers related to the stochastic modellingof disability insurance. In the first paper, we propose a stochastic semi-Markovian framework for disability modelling in a multi-period discrete-time setting. The logistic transforms of disability inception and recovery probabilities are modelled by means of stochastic risk factors and basis functions, using counting processes and generalized linear models. The model for disability inception also takes IBNR claims into consideration. We fit various versions of the models into Swedish disability claims data. In the second paper, we consider a large, homogeneous portfolio oflife or disability annuity policies. The policies are assumed to be independent conditional on an external stochastic process representing the economic environment. Using a conditional law of large numbers, we establish the connection between risk aggregation and claims reserving for large portfolios. Further, we derive a partial differential equation for moments of present values. Moreover, we show how statistical multi-factor intensity models can be approximated by one-factor models, which allows for solving the PDEs very efficiently. Finally, we givea numerical example where moments of present values of disabilityannuities are computed using finite difference methods.QC 20131204
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Currie, James. "Stochastic modelling of TCR binding." Thesis, University of Leeds, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.590430.
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A fundamental process in the immune response to infection is the activation of T cells following contact with antigen presenting cells. This activation occurs after T cell receptors on the surface of T cells bind to immunogenic peptides expressed on the surface of antigen presenting cells. The binding of T cell receptors to ligands not only leads to the activation of T cells, it is also key to T cell selection in the thymus and the maintenance of a diverse T cell receptor repertoire. T cell receptor bindings are converted into a signal which activates a T cell but there is no universal theory which governs this process. There is experimental evidence to suggest that receptor-ligand bindings must be sufficiently long to elicit a T cell response. and that counting devices in the T cell work to allow signal accumulation, decoding and translation into biological responses. In view of these results, this thesis uses mathematical models to explore the timescales associated with T cell responses. A stochastic criterion that T cell responses occur after N receptor-ligand complexes have been bound for at least a dwell time, T, each, is used. The first model of receptor-ligand binding, in conjunction with the stochastic criterion, supports the affinity threshold hypothesis for thymic selection and agrees with the experimentally established ligand hierarchy for thymic negative selection. The initial model of ligand-receptor binding is then extended to include feedback responses, bivalent receptor binding and ligand diffusion through the immunological synapse. By including these mechanisms, the models agree with an array of experimental hypotheses which include: T cells exhibit a digital response to ligand. bivalent T cell receptor engagement stabilises receptor-ligand bindings and one ligand is sufficient to elicit a T cell response.
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Tsang, Wai-yin, and 曾慧賢. "Aspects of modelling stochastic volatility." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31223515.
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Ferreira, Jose Antonio de Sousa Jorge. "Some contributions to stochastic modelling." Thesis, University of Sheffield, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.312790.
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Luo, Yang. "Stochastic modelling in biological systems." Thesis, University of Cambridge, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.610145.
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Dalton, Rowan. "Modelling stochastic multi-curve basis." Master's thesis, University of Cape Town, 2017. http://hdl.handle.net/11427/27102.
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As a consequence of the 2007 financial crisis, the market has shifted towards a multi-curve approach in modelling the prevailing interest rate environment. Currently, there is a reliance on the assumption of deterministic- or constant-basis spreads. This assumption is too simplistic to describe the modern multi-curve environment and serves as the motivation for this work. A stochastic-basis framework, presented by Mercurio and Xie (2012), with one- and two-factor OIS short-rate models is reviewed and implemented in order to analyse the effect of the inclusion of stochastic-basis in the pricing of interest rate derivatives. In order to preclude the existence of negative spreads in the model, a constraint on the spread model parameters is necessary. The inclusion of stochastic-basis results in a clear shift in the terminal distributions of FRA and swap rates. In spite of this, stochastic-basis is found to have a negligible effect on cap/floor and swaption prices for the admissible spread model parameters. To overcome challenges surrounding parameter estimation under the framework, a rudimentary calibration procedure is developed, where the spread model parameters are estimated from historical data; and the OIS rate model parameters are calibrated to a market swaption volatility surface.
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Tsang, Wai-yin. "Aspects of modelling stochastic volatility /." Hong Kong : University of Hong Kong, 2000. http://sunzi.lib.hku.hk/hkuto/record.jsp?B22078952.
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Sahoo, Anita. "Stochastic modelling of tumour growth." Thesis, Queen's University Belfast, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.501402.
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Malada, Awelani. "Stochastic reliability modelling for complex systems." Thesis, Pretoria : [s.n.], 2006. http://upetd.up.ac.za/thesis/available/etd-10182006-170927.
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Alisar, Ibrahim. "Stochastic Modelling Of Wind Energy Generation." Master's thesis, METU, 2012. http://etd.lib.metu.edu.tr/upload/12614930/index.pdf.
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In this thesis work, electricty generation modeling of the wind energy -one type of the
renewable energy sources- is studied. The wind energy characteristics and the distribution of
wind speed in a specific region is also examined. In addition, the power curves of the wind
turbines are introduced and the relationship between the wind speed and wind power is
explained. The generation characteristics of the wind turbines from various types of
producers are also investigated. In this study, the main wind power forecasting methods are
presented and the advantages and disadvantages of the methods are analyzed. The physical
approaches, statistical methods and the Artificial Neural Network (ANN) methods are
introduced. The parameters that affect the capacity factor, the total energy generation and the
payback period are examined. In addition, the wind turbine models and their effect on the
total energy generation with different wind data from various sites are explained. As a part
of this study, a MATLAB-based software about wind speed and energy modelling and
payback period calculation has been developed. In order to simplify the calculation process,
a Graphical User Interface (GUI) has been designed. In addition, a simple wind energy
persistence model for wind power plant operator in the intra-day market has been developed.
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Menz, William Jefferson. "Stochastic modelling of silicon nanoparticle synthesis." Thesis, University of Cambridge, 2014. https://www.repository.cam.ac.uk/handle/1810/245146.
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This thesis presents new methods to study the aerosol synthesis of nano-particles and a new model to simulate the formation of silicon nanoparticles. Population balance modelling is used to model nanoparticle synthesis and a stochastic numerical method is used to solve the governing equations. The population balance models are coupled to chemical kinetic models and offer insight into the fundamental physiochemical processes leading to particle formation. The first method developed in this work is a new mathematical expression for calculating the rate of Brownian coagulation with stochastic weighted algorithms (SWAs). The new expression permits the solution of the population balance equations with SWAs using a computationally-efficient technique of majorant rates and fictitious jumps. Convergence properties and efficiency of the expression are evaluated using a detailed silica particle model. A sequential-modular algorithm is subsequently presented which solves networks of perfectly stirred reactors with a population balance model using the stochastic method. The algorithm is tested in some simple network configurations, which are used to identify methods through which error in the stochastic solution may be reduced. It is observed that SWAs are useful in preventing accumulation of error in reactor networks. A new model for silicon nanoparticle synthesis is developed. The model includes gas-phase reactions describing silane decomposition, and a detailed multivariate particle model which tracks particle structure and composition. Systematic parameter estimation is used to fit the model to experimental cases. Results indicated that the key challenge in modelling silicon systems is obtaining a correct description of the particle nucleation process. Finally, the silicon model is used in conjunction with the reactor network algorithm to simulate the start-up of a plug-flow reactor. The power of stochastic methods in resolving characteristics of a particle ensemble is highlighted by investigating the number, size, degree of sintering and polydispersity along the length of the reactor.
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Strubbe, Stefan Nicolaas. "Compositional modelling of stochastic hybrid systems." Enschede : University of Twente [Host], 2005. http://doc.utwente.nl/50865.
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Bujorianu, Manuela-Luminita. "Stochastic hybrid system : modelling and verification." Thesis, University of Stirling, 2005. http://hdl.handle.net/1893/3451.
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Hybrid systems now form a classical computational paradigm unifying discrete and continuous system aspects. The modelling, analysis and verification of these systems are very difficult. One way to reduce the complexity of hybrid system models is to consider randomization. The need for stochastic models has actually multiple motivations. Usually, when building models complete information is not available and we have to consider stochastic versions. Moreover, non-determinism and uncertainty are inherent to complex systems. The stochastic approach can be thought of as a way of quantifying non-determinism (by assigning a probability to each possible execution branch) and managing uncertainty. This is built upon to the - now classical - approach in algorithmics that provides polynomial complexity algorithms via randomization. In this thesis we investigate the stochastic hybrid systems, focused on modelling and analysis. We propose a powerful unifying paradigm that combines analytical and formal methods. Its applications vary from air traffic control to communication networks and healthcare systems. The stochastic hybrid system paradigm has an explosive development. This is because of its very powerful expressivity and the great variety of possible applications. Each hybrid system model can be randomized in different ways, giving rise to many classes of stochastic hybrid systems. Moreover, randomization can change profoundly the mathematical properties of discrete and continuous aspects and also can influence their interaction. Beyond the profound foundational and semantics issues, there is the possibility to combine and cross-fertilize techniques from analytic mathematics (like optimization, control, adaptivity, stability, existence and uniqueness of trajectories, sensitivity analysis) and formal methods (like bisimulation, specification, reachability analysis, model checking). These constitute the major motivations of our research. We investigate new models of stochastic hybrid systems and their associated problems. The main difference from the existing approaches is that we do not follow one way (based only on continuous or discrete mathematics), but their cross-fertilization. For stochastic hybrid systems we introduce concepts that have been defined only for discrete transition systems. Then, techniques that have been used in discrete automata now come in a new analytical fashion. This is partly explained by the fact that popular verification methods (like theorem proving) can hardly work even on probabilistic extensions of discrete systems. When the continuous dimension is added, the idea to use continuous mathematics methods for verification purposes comes in a natural way. The concrete contribution of this thesis has four major milestones: 1. A new and a very general model for stochastic hybrid systems; 2. Stochastic reachability for stochastic hybrid systems is introduced together with an approximating method to compute reach set probabilities; 3. Bisimulation for stochastic hybrid systems is introduced and relationship with reachability analysis is investigated. 4. Considering the communication issue, we extend the modelling paradigm.
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McNaught, Kenneth R. "Extensions of stochastic combat modelling methodology." Thesis, Cranfield University, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.266484.
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Pham, Duy. "Markov-functional and stochastic volatility modelling." Thesis, University of Warwick, 2012. http://wrap.warwick.ac.uk/55161/.
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In this thesis, we study two practical problems in applied mathematical fi nance. The first topic discusses the issue of pricing and hedging Bermudan swaptions within a one factor Markov-functional model. We focus on the implications for hedging of the choice of instantaneous volatility for the one-dimensional driving Markov process of the model. We find that there is a strong evidence in favour of what we term \parametrization by time" as opposed to \parametrization by expiry". We further propose a new parametrization by time for the driving process which takes as inputs into the model the market correlations of relevant swap rates. We show that the new driving process enables a very effective vega-delta hedge with a much more stable gamma profile for the hedging portfolio compared with the existing ones. The second part of the thesis mainly addresses the topic of pricing European options within the popular stochastic volatility SABR model and its extension with mean reversion. We investigate some effcient approximations for these models to be used in real time. We first derive a probabilistic approximation for three different versions of the SABR model: Normal, Log-Normal and a displaced diffusion version for the general constant elasticity of variance case. Specifically, we focus on capturing the terminal distribution of the underlying process (conditional on the terminal volatility) to arrive at the implied volatilities of the corresponding European options for all strikes and maturities. Our resulting method allows us to work with a variety of parameters which cover long dated options and highly stress market condition. This is a different feature from other current approaches which rely on the assumption of very small total volatility and usually fail for longer than 10 years maturity or large volatility of volatility. A similar study is done for the extension of the SABR model with mean reversion (SABR-MR). We first compare the SABR model with this extended model in terms of forward volatility to point out the fundamental difference in the dynamics of the two models. This is done through a numerical example of pricing forward start options. We then derive an effcient probabilistic approximation for the SABRMR model to price European options in a similar fashion to the one for the SABR model. The numerical results are shown to be still satisfactory for a wide range of market conditions.
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Powell, Jonathan. "Stochastic modelling of atmospheric gravity waves." Thesis, University of Edinburgh, 2004. http://hdl.handle.net/1842/15652.
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Internal gravity waves have an important effect on the large-scale circulation of the middle atmosphere, which is conditioned by the deposition of momentum due to their breaking. The propagation of gravity waves is influenced by the properties of the background wind. This thesis examines this influence: it uses stochastic techniques to study gravity wave propagation through a randomly fluctuating background wind. It begins by describing general features of the atmosphere and gravity wave propagation. The basic equations of fluid flow within the atmosphere are derived. These lead via the WKB approximation to a dispersion relation and to ray equations for gravity wave propagation. Propagation equations, such as the ray equations and dispersion relation, are derived in a general context. The notion of a Wigner matrix is introduced, and this is used to derive transport equations for a general Hamiltonian system that may contain random components. These results generalise earlier works by Ryzhik and Guo and Wang. Atmospheric gravity waves are described as an application and the equations derived via the WKB approximation are recovered. The major factor influencing the distribution of gravity waves is the spread of their wavenumber as they propagate through a wind. This is described by the Doppler spreading model. A one-dimensional system with a randomly fluctuating background wind, dependent on altitude only, is considered. The model revisits that of Souprayen by using an Ornstein-Uhlenbeck process to describe the wind. Simple equations for the energy spectrum induced by gravity waves are derived. Analytic forms of the energy spectrum are given and features of the spectrum such as the m-3 spectral tail (where m is the vertical wavenumber), central wavenumber and scaling with the Brunt-Väisälä frequently are found to be consistent with observations. An equation for the force on the background, induced by gravity wave breaking is also derived.
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He, Enuo. "Stochastic modelling of the cell cycle." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:04185cde-85af-4e24-8d06-94b865771cf1.
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Precise regulation of cell cycle events by the Cdk-control network is essential for cell proliferation and the perpetuation of life. The unidirectionality of cell cycle progression is governed by several critical irreversible transitions: the G1-to-S transition, the G2-to-M transition, and the M-to-G1 transition. Recent experimental and theoretical evidence has pulled into question the consensus view that irreversible protein degradation causes the irreversibility of those transitions. A new view has started to emerge, which explains the irreversibility of cell cycle transitions as a consequence of systems-level feedback rather than of proteolysis. This thesis applies mathematical modelling approaches to test this proposal for the Mto- G1 transition, which consists of two consecutive irreversible substeps: the metaphase-to-anaphase transition, and mitotic exit. The main objectives of the present work were: (i) to develop deterministic models to identify the essential molecular feedback loops and to examine their roles in the irreversibility of the M-to-G1 transition; (ii) to present a straightforward and reliable workflow to translate deterministic models of reaction networks into stochastic models; (iii) to explore the effects of noise on the cell cycle transitions using stochastic models, and to compare the deterministic and the stochastic approaches. In the first part of this thesis, I constructed a simplified deterministic model of the metaphase-to-anaphase transition, which is mainly regulated by the spindle assembly checkpoint (the SAC). Based on the essential feedback loops causing the bistability of the transition, this deterministic model provides explanations for three open questions regarding the SAC: Why is the SAC not reactivated when the kinetochore tension decreases to zero at anaphase onset? How can a single unattached kinetochore keep the SAC active? How is the synchronized and abrupt destruction of cohesin triggered? This deterministic model was then translated into a stochastic model of the SAC by treating the kinetochore microtubule attachment at prometaphase as a noisy process. The stochastic model was analyzed and simulation results were compared to the experimental data, with the aim of explaining the mitotic timing regulation by the SAC. Our model works remarkably well in qualitatively explaining experimental key findings and also makes testable predictions for different cell lines with very different number of chromosomes. The noise generated from the chemical interactions was found to only perturb the transit timing of the mitotic events, but not their ultimate outcomes: all cells eventually undergo anaphase, however, the time required to satisfy the SAC differs between cells due to stochastic effects. In the second part of the thesis, stochastic models of mitotic exit were created for two model organisms, budding yeast and mammalian cells. I analyzed the role of noise in mitotic exit at both the single-cell and the population level. Stochastic time series simulations of the models are able to explain the phenomenon of reversible mitotic exit, which is observed under specific experimental conditions in both model organisms. In spite of the fact that the detailed molecular networks of mitotic exit are very different in budding yeast and mammalian cells, their dynamic properties are similar. Importantly, bistability of the transitions is successfully captured also in the stochastic models. This work strongly supports the hypothesis that uni-directional cell cycle progression is a consequence of systems-level feedback in the cell cycle control system. Systems-level feedback creates alternative steady states, which allows cells to accomplish irreversible transitions, such as the M-to-G1 transition studied here. We demonstrate that stochastic models can serve as powerful tools to capture and study the heterogeneity of dynamical features among individual cells. In this way, stochastic simulations not only complement the deterministic approach, but also help to obtain a better understanding of mechanistic aspects. We argue that the effects of noise and the potential needs for stochastic simulations should not be overlooked in studying dynamic features of biological systems.
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Obisesan, Abayomi. "Stochastic damage modelling of ship collisions." Thesis, University of Aberdeen, 2017. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=231845.
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Ship collision accidents are rare events but pose huge threat to human lives, assets, and the environment. Collision resistance of ships is usually assessed in terms of ship structural response such as member displacement, energy dissipation and the extent of damage. Many researchers have sought for effective models that compute ship stochastic response during collisions by considering the variability of collision scenario parameters. However, the models were limited by the capability of the collision computational models and did not completely capture collision scenario, and material and geometric uncertainties. In addition, the simplified models capturing the input-response relationships of the ship structural impact mechanics are in implicit forms which makes them unsuitable for assessing the performance of structural design specifications in collisions. Furthermore, with increasing ship passages in the Arctic region, the probabilities of ship-iceberg interactions are increasing, highlighting the need to focus on risk based ship designs. In this research, a conceptual stochastic modelling framework is developed for performance characterisation and quantitative risk assessment of ship-ship and ship-iceberg collisions. In this direction, an interface for automated stochastic finite element computations was developed to model ship structural resistance in reference collision scenarios. The stochastic structural response was characterised based on the onset of the ship structural failure. The focus was initially on ship-ship collisions to quantify the uncertainties experimentally and to characterise the performance for a variety of striking ships. The framework was then extended to consider probabilistic performance measures in ship-iceberg collisions. The computationally intensive collision response models were captured with efficient surrogate representations so that the performance measures can be obtained with gradient based reliability approaches. The most probable input design sets for the response distribution were sampled with Latin Hypercube models. The probabilistic performance measures were also combined with available collision frequency models from literature for risk computations and to demonstrate the risk tolerance measures. The framework underlines the significance of different risk components, providing valuable guidance for improving risk-based ship designs. Although, a double-hull crude oil carrier is presented as the struck ship, the approach can be readily extended to characterise the performance and risk of other ship structures in collisions.
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Albertyn, Martin. "Generic simulation modelling of stochastic continuous systems." Thesis, Pretoria : [s.n.], 2004. http://upetd.up.ac.za/thesis/available/etd-05242005-112442.
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Barbu, Monica Constanta. "Stochastic modelling applications in continuous time finance /." [St. Lucia, Qld.], 2004. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe18290.pdf.
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de, la Cruz Moreno Roberto. "Stochastic multi-scale modelling of tumour growth." Doctoral thesis, Universitat Autònoma de Barcelona, 2017. http://hdl.handle.net/10803/457590.
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El cáncer es una de las principales causas de muerte en el mundo. A pesar de todos los recursos invertidos en la investigación para el desarrollo de nuevas terapias, los tratamientos más usados en la lucha contra el cáncer siguen siendo terapias inespecíficas (cirugía, radioterapia y quimioterapia) que afectan tanto a las células cancerígenas como a las sanas. En contraposición a estas terapias inespecíficas, se ha utilizado un enfoque alternativo en la medicina, que se conoce como magic bullet, para guiar el desarrollo de nuevas terapias. El concepto consiste en encontrar un fármaco con un objetivo específico (gen, proteína, etc.) implicado en una etapa particular del desarrollo de la enfermedad que mate sólo a las células no saludables y deje las células normales ilesas. Aunque no es un enfoque nuevo, su impacto en enfermedades complejas de momento ha sido discreto.
La falta de efectividad del enfoque magic bullet plantea dos preguntas: ¿Por qué falla este enfoque en el caso del cáncer? y ¿qué podemos hacer para mejorar su eficacia?.
El comportamiento y las características de los sistemas biológicos están influenciados por una compleja red de interacciones entre genes y productos genéticos que regulan la expresión génica. Las estructuras dinámicas no lineales y de gran dimensión han sufrido cambios evolutivos por selección natural. A medida que avanza el tiempo, la resiliencia del fenotipo frente a las alteraciones genéticas aumenta permitiendo la canalización (genética), es decir, la capacidad para ser más robustos. Particularmente, los tumores malignos aprovechan estas propiedades y estructuras para aumentar su potencial proliferativo y resistir terapias. Las capas de complejidad involucradas dentro del sistema inducen dificultades para predecir el efecto de una perturbación aplicada en el sistema. Con el fin de abordar con éxito estos problemas, una se ha llevado a cabo una gran cantidad de investigación en el análisis y el desarrollo de modelos de escalas múltiples. Estos modelos incorporan diferentes sub-modelos que corresponden a diferentes niveles biológicos, de manera que el comportamiento global del tejido puede ser analizado como una propiedad emergente de los elementos acoplados.
Se sabe que los modelos de escalas múltiples presentan una series de problemas. El objetivo principal de esta tesis es la formulación y el análisis de un modelo estocástico de escalas múltiples de la dinámica de poblaciones celulares para arrojar luz sobre:
• Los efectos del acoplamiento entre fluctuaciones intrínsecas a nivel intracelular y poblacional. Nuestro objetivo es establecer cómo las diferentes fuentes de ruido afectan las propiedades globales de los tumores en crecimiento, como la velocidad de invasión.
• Determinar los límites de coarse-grained de estos modelos para que los parámetros de los modelos de escalas múltiples puedan agruparse en un número menor de parámetros. Esto facilitaría la tarea de estimación de parámetros.
• Formular métodos híbridos que nos permitan simular sistemas más grandes sin perder ninguna de las características esenciales del sistema de escalas múltiples.
Con este fin, establecemos una manera sistemática de considerar el ruido en estos modelos.Cancer is one of the principal causes of death in the world . Despite all the resources invested in research for the development of new targeted therapies, the most used treatments to fight cancer continue to be non-specific therapies, such as surgery, radiotherapy and chemotherapy, that affect both healthy and cancer cells. In contraposition to unspecific therapies, an alternative approach has been used in medicine that is commonly referred to as the magic bullet to guide the development of new targeted therapies. The concept consists of finding a drug with a specific target (gene, protein, etc.) implicated at a particular stage of development of the disease by killing just unhealthy cells whilst leaving normal cells unharmed. Although it is not a new approach, its impact on complex diseases has been discreet . The lack of effectiveness of the magic bullet approach brings about two questions: Why does that approach fail in the case of cancer? and What do we do to improve its effectiveness? . The behaviour and traits of biological systems are influenced by a complex network of interactions between genes and gene products which regulate gene expression. The non-linear, high-dimensional dynamical structures have undergone evolutionary changes by natural selection. As time progresses, the resilience of the phenotype against genetic alteration increases allowing canalisation (the ability to become more robust). Particularly, in malignancies these properties and structures are exploited by the tumour to increase its proliferative potential and resist therapies. The layers of complexities involved within the system, induce difficulties in predicting the effect of a perturbation applied in the system. In order to successfully address the issues, a huge amount of research has been undertaken involving analysis and development of multi-scale models. These models incorporate different sub-models corresponding to different biological levels such that the global tissue behaviour could be analysed as an emergent property of the coupled elements. Multi-scale models are known to be affected by a number of issues. The principal aim of this thesis is the formulation and analysis of stochastic multi-scale model of the dynamics of cellular populations that shed light on: • The effects of coupling between intrinsic fluctuations at the intracellular and population levels. We aim to establish how the different sources of noise affect global properties of growing tumours, such as the speed of invasion. • Derive coarse-grained limits of these models so that the parameters of the multi- scale models can be lumped together into a smaller number of parameters. This will facilitate the task of parameter estimation. • To formulate hybrid methods which allow us to simulate larger systems while losing none of the essential features of the multi-scale system. To this end, we establish a systematic way to consider the noise in multi-scale models.
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Chaleeraktrakoon, Chavalit. "Stochastic modelling and simulation of streamflow processes." Thesis, McGill University, 1995. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=28704.
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The main objectives of this research are to propose a general stochastic method for determining analytically the distribution of flood volume, and to develop a simulation procedure for generating synthetic multiseason streamflows at different sites simultaneously. The research study is divided into two parts: (a) First, a general stochastic model is proposed to derive analytically the probability distribution function for flood volume. The volume of a flood is defined as the sum of an unbroken sequence of consecutive daily flows above a given truncation level. Analytical expressions were then derived for the exact distribution of flood volume for various cases in which successive flow exceedances can be assumed to be either independent or correlated, and the cumulative flow exceedance can be considered to be independent or dependent of the corresponding flood duration. The proposed stochastic method is more general and more flexible than empirical fitting approach because it can take explicitly into account different stochastic properties inherent in the underlying streamflow process. Results of a numerical application have shown that the proposed model could provide a very good fit between observed and theoretical results. Further, in the estimation of flood volume distribution, it has been found that the effect of the serial correlation property of the flow series is not significant as compared to the impact due to the dependence between flood volume and corresponding duration. Finally, it has been demonstrated that the simplistic assumption of triangular flood hydrograph shape, as usually appeared in previous studies, is not necessary in the estimation of flood volume distribution. (b) Second, a multivariate stochastic simulation approach is proposed for generating synthetic seasonal streamflow series at a single location or at many different locations concurrently. The suggested simulation scheme is based on the combination of the singular value decomposition
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Gregotski, Mark Edward. "Fractal stochastic modelling of airborne magnetic data." Thesis, McGill University, 1989. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=74300.
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Airborne magnetic field data exhibit downward continued power spectra of the form $1/f sp beta$ (where f is the spatial frequency and $ beta$ is a non-negative real number). This form of spectrum is observed for magnetic data recorded over a range of sampling scales from various areas of the Canadian Shield. Two scaling regimes have been discovered. The first has a $ beta$ value near 3 for wavelengths $ sbsp{ sim}{$25 km. These results suggest a "variable fractal" description of the distribution of near-surface magnetic sources.From a data modelling viewpoint, the magnetic measurements are derived from a linear superposition of a deterministic system function and a stochastic excitation process. A symmetric operator corresponds to the system function, and the near-surface magnetic source distribution represents the excitation process. The deconvolution procedure assumes an autoregressive (AR) system function and proceeds iteratively using bi-directional AR (BDAR) filtering in one dimension, which is extended to four-pass AR filtering in two dimensions. The traditional assumption of a spectrally white innovation is used in the deconvolution procedure. The data are modified prior to deconvolution by a Fourier domain prewhitening technique, to account for the long wavelength content of the fractal innovation. Deconvolution of the modified data produces the system function, which is removed from the original data to produce the near-surface magnetic source distribution. This distribution serves as a susceptibility map which can be used for enhancing magnetic field anomalies and geological mapping. Thus, the statistical descriptions of near-surface magnetic sources are useful for modelling airborne magnetic data in "shield-type" geologic environments.
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Turfus, C. "Stochastic modelling of turbulent dispersion near surfaces." Thesis, University of Cambridge, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.333097.
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Li, Guangquan. "Stochastic modelling of carcinogenesis : theory and application." Thesis, Imperial College London, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.486378.
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Cancer is a group of diseases characterized by autonomous, uncontrollable cell proliferation, evasion of cell death, self-construction of oxygen and nutrient supply and spreading of cancerous cells through metastasis. It is vital to elucidate pathways that underlie the cancer process. Mechanistic cancer models, to this extent, attempt to relate the occurrence: of malignant neoplasm to diverse risk factors such as genetic alterations, susceptibility of individuals and exogenous and endogenous carcinogenic exposures. The main objectives of this thesis are to examine the validity of the two-hit hypothesis for retinoblastoma (Knudson, 1971, PNAS (68) 820-23), to unify multiple types of genomic instability and to further assess the role of genomic instability played in the process of carcinogenesis. I shall also explore characteristics of existing mechanistic cancer models. This thesis begins with a survey' of basic cancer biology and existing mechanistic models. Utilizing a fully-stochastic two-stage clonal expansion model, the thesis specifically assesses the validity of the two-hit theory for retinoblastoma-(RB), a childhood ocular malignancy. Comparison of fits of a variety of models (in particular those with up to three mutations) to a population-based RB dfltaset demonstrates the superior fit of the two-stage model to others. This result strongly suggests both the necessity and sufficiency of the two RBI mutations to initiate RB and hence validates the two-hit theory. The thesis goes on to develop a comprehensive,. framework to incorporate multiple types of genomic instability, characterized by-numerous numerical and structural damages exhibiting in the cancer cell genome. This generalized model embraces���·;most, if not all, of the existing MVK-type models. Specific forms of the model are fitted to U.S. white American colon cancer incidence data. Based on comparison of fits to the population-based data, there is little evidence to support the hypothesis that models with more than one type of genomic instability fits better than those with a single type of genomic instability. Since the age-specific incidence data may not possess sufficient information for model discrimination, further investigation is required. The remainder ofthis thesis is concerned with two theoretical aspects. To facilitate a Bayesian implementation for data fitting, a flexible blocking algorithm is developed. In the presence of parameter correlation, the algorithm considerably improves the performance of the Markov chain Monte Carlo simulations. In addition, following a similar approach of Heidenreich et al. (1997, Risk Anal. (17) 391-399), the maximum number of identifiable parameters in the proposed cancer model WIth r types of genomIc InstabIlIty IS r +1 less than the number of biologically-based parameters.
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Huang, Hong-Chih. "Stochastic modelling and control of pension plans." Thesis, Heriot-Watt University, 2000. http://hdl.handle.net/10399/549.
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Serrano, Rico Alan Edwin. "Stochastic Information Technology Modelling for Business Processes." Thesis, Brunel University, 2002. http://bura.brunel.ac.uk/handle/2438/2035.
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Business Processes (BP) and Information Technology (IT) are two areas that work very closely in helping organisations to keep or retain competitive advantage. Therefore, design in these areas should consider the advantages provided by, and the limitations that each of these domains imposes on each other. BP design tries to ensure that IT specifications are considered during the design of BP. Similarly, Information Systems (IS) design attempts to capture organisational needs, known as IS functional and Non-Functional Requirements (NFR), in order to meet the organisational goals. Despite this, BP and IT modelling techniques barely depict the way IT may affect BP performance or vice versa. For example, Business Process Simulation (BPS) is one of the modelling techniques that has been increasingly used to support process design. The performance measurements obtained from BPS models, though, are obtained considering only organisational issues, and thus cannot be used to assess the impact that IT may have on process performance. Similarly, IT modelling techniques do not provide IS performance measurements, and hence cannot depict the way IS may improve BP performance. The relationship between BP and IT can be alternatively described in terms of the relationships between BP, IS and Computer Networks (CN). By looking at the parameters that govern these relationships a simulation framework was developed, namely ASSESS-IT, that develops simulation models that provide performance measurements of BP, IS and CN, and thus can reflect the impact that IT (IS and CN) may have on BP performance. This research uses a case study to test the proposed framework (theory testing), to understand the way BP, IS, and CN domains interact (discovery), and to propose alternative theories to solve the problems found (theory building). The experimentation with the ASSESS-IT framework suggests that in order to portray the impact that IT may have on BP, analysts in these domains should first identify those performance specifications that describe how well the IS delivers its functionality (also known as non-functional requirements). It was found that when the IS does not depend on determined response time, the relationships between BP, IS and CN can be assessed using only the relationship between BP and IS. An alternative simulation framework, namely BPISS, is proposed to produce BPS models that provide performance measurements of BP and IS. Thus, BP and IT analysts can investigate the impact that a given IS design may have on BP performance, and identify a better BP and IS solution.
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Conway, Eunan Martin. "Stochastic modelling and forecasting of solar radiation." Thesis, Northumbria University, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.367414.
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Bradley, Jeremy Thomas. "Towards reliable modelling with stochastic process algebras." Thesis, University of Bristol, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302166.
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Graham, D. P. "Stochastic modelling and analysis of construction processes." Thesis, University of Edinburgh, 2005. http://hdl.handle.net/1842/12054.
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Construction projects frequently overrun and finish over budget; in part due to the lack of control that construction practitioners have over the construction schedule at a process level. Planning methods such as CPM are not of sufficient detail to allow a practitioner to plan a process to maximise its performance. Thus the aim of this research was to develop a practical, computer-based model to enable practitioners to plan projects at a process level and hence improve their projects. This research has focused upon a specific type of process - those that are stochastic and cyclical. Such processes are difficult to predict and hence control, and they are widespread throughout construction projects. Examples are crane operations, formwork erection and scaffold erection. Initially, a focus was placed on the ready-mixed concrete (RMC) supply process. A discrete event simulation (DES) model of this process was developed and validated, based upon real project data. This model could not provide accurate estimates of the process due to the requirement that a user define the probability distributions that represent the process. This is a complex requirement for a practitioner, the issue became known as the complexity problem and a solution was sought using case-based reasoning (CBR). CBR provides solutions to new problems using knowledge from past ones - exactly what a practitioner was doing in the above simulation model. CBR was shown to be capable of solving the complexity problem. A hybrid model, CBRSim, was formed to fulfil the original aim of this thesis. CBRSim works by: CBR selecting probability distributions (based on user input) that are used in a DES model to accurately recreate the process. CBRSim was validated and modelled the process to within +/- 3% accuracy. CBRSim was then applied to another stochastic and cyclical construction process: earthmoving. CBRSim was found to be more accurate in estimating earthmoving productivity than RMC supply, thus providing an indication of a generic modelling capability.
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Zverovich, Victor. "Modelling and solution methods for stochastic optimisation." Thesis, Brunel University, 2011. http://bura.brunel.ac.uk/handle/2438/5922.
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In this thesis we consider two research problems, namely, (i) language constructs for modelling stochastic programming (SP) problems and (ii) solution methods for processing instances of different classes of SP problems. We first describe a new design of an SP modelling system which provides greater extensibility and reuse. We implement this enhanced system and develop solver connections. We also investigate in detail the following important classes of SP problems: singlestage SP with risk constraints, two-stage linear and stochastic integer programming problems. We report improvements to solution methods for single-stage problems with second-order stochastic dominance constraints and two-stage SP problems. In both cases we use the level method as a regularisation mechanism. We also develop novel heuristic methods for stochastic integer programming based on variable neighbourhood search. We describe an algorithmic framework for implementing decomposition methods such as the L-shaped method within our SP solver system. Based on this framework we implement a number of established solution algorithms as well as a new regularisation method for stochastic linear programming. We compare the performance of these methods and their scale-up properties on an extensive set of benchmark problems. We also implement several solution methods for stochastic integer programming and report a computational study comparing their performance. The three solution methods, (a) processing of a single-stage problem with second-order stochastic dominance constraints, (b) regularisation by the level method for two-stage SP and (c) method for solving integer SP problems, are novel approaches and each of these makes a contribution to knowledge.
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Szekely, Tamas. "Stochastic modelling and simulation in cell biology." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:f9b8dbe6-d96d-414c-ac06-909cff639f8c.
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Modelling and simulation are essential to modern research in cell biology. This thesis follows a journey starting from the construction of new stochastic methods for discrete biochemical systems to using them to simulate a population of interacting haematopoietic stem cell lineages. The first part of this thesis is on discrete stochastic methods. We develop two new methods, the stochastic extrapolation framework and the Stochastic Bulirsch-Stoer methods. These are based on the Richardson extrapolation technique, which is widely used in ordinary differential equation solvers. We believed that it would also be useful in the stochastic regime, and this turned out to be true. The stochastic extrapolation framework is a scheme that admits any stochastic method with a fixed stepsize and known global error expansion. It can improve the weak order of the moments of these methods by cancelling the leading terms in the global error. Using numerical simulations, we demonstrate that this is the case up to second order, and postulate that this also follows for higher order. Our simulations show that extrapolation can greatly improve the accuracy of a numerical method. The Stochastic Bulirsch-Stoer method is another highly accurate stochastic solver. Furthermore, using numerical simulations we find that it is able to better retain its high accuracy for larger timesteps than competing methods, meaning it remains accurate even when simulation time is speeded up. This is a useful property for simulating the complex systems that researchers are often interested in today. The second part of the thesis is concerned with modelling a haematopoietic stem cell system, which consists of many interacting niche lineages. We use a vectorised tau-leap method to examine the differences between a deterministic and a stochastic model of the system, and investigate how coupling niche lineages affects the dynamics of the system at the homeostatic state as well as after a perturbation. We find that larger coupling allows the system to find the optimal steady state blood cell levels. In addition, when the perturbation is applied randomly to the entire system, larger coupling also results in smaller post-perturbation cell fluctuations compared to non-coupled cells. In brief, this thesis contains four main sets of contributions: two new high-accuracy discrete stochastic methods that have been numerically tested, an improvement that can be used with any leaping method that introduces vectorisation as well as how to use a common stepsize adapting scheme, and an investigation of the effects of coupling lineages in a heterogeneous population of haematopoietic stem cell niche lineages.
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Day, Mark Stephen. "Stochastic modelling of lymphocyte dynamics and interactions." Thesis, University of Leeds, 2013. http://etheses.whiterose.ac.uk/5274/.
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The immune system protects the body against invading pathogens. For an immune response to occur, a T cell must encounter a rare antigen-presenting-cell (APC) presenting its cognate antigen. The time it takes for this encounter depends upon how quickly the T cell is moving, as well as how many APCs carrying the T cells cognate antigen are present. First passage processes are used to derive an equation for the encounter time of a T cell with one of N APCs. Using this time, a rate of encounter is established, and used throughout this thesis. The encounter rate is dependent upon the radius of the lymph node, the effective radius of the APC, and the diffusivity of the T cell. However, the diffusivity of T cells has not been clearly established. In vivo imaging data is used to develop a systematic method for determining the diffusivity of a population of T cells. Due to in vivo imaging experiments having a limited sized imaging volume, a confinement effect is observed. The expected squared displacement of imaged cells is calculated, and the level at which a confinement plateau should be observed is determined. T cell activation, in lymph nodes, relies upon encounters with APCs, but the number of APCs required to initiate a T cell response is currently unknown. Using mathematical models, in combination with experimental work, the probability of T cell-APC encounters can be quantified. The probability of a T cell, residing in the lymph node for twenty four hours, to interact with APCs is calculated. Extrapolating the developed models to later times and lower cell numbers than can be achieved experimentally, a minimum number of APCs required to initiate a T cell response, for typical human T cell precursor frequencies, is estimated. It has been proposed that regulatory T cells suppress effector T cells via a three way interaction with APCs, as a method of preventing autoimmunity. A stochastic model of these interactions is developed and explored. The steady state of the system is found to depend upon the rate of encounter of T cells and APCs, as well as the number of APCs. Stochastic effects are observed in the model, which affect the state of the system, and are not observed in a deterministic approach. Interactions between T cells and APCs, in lymph nodes, are crucial for initiating cell-mediated adaptive immune responses. However, how these interactions cause activation of the T cells is not yet fully understood. Three hypotheses have been proposed for the method of T cell activation. These hypotheses are investigated, and models developed, in an attempt to quantify the observed stages of the activation process. It is found that experimental results can, in part, be explained by a probabilistic approach.
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Morgan, Meirion. "Reaction problems in stochastic chemistry." Thesis, University of Oxford, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.301256.
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Ha, Minh Thien. "Modelling of stochastic and quasi-periodic texture images /." [S.l.] : [s.n.], 1989. http://library.epfl.ch/theses/?nr=804.
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Van, Loon Jasper. "Functional and stochastic modelling of satellite gravity data /." Delft : NCG Nederlandse Commissie voor Geodesie, 2008. http://opac.nebis.ch/cgi-bin/showAbstract.pl?u20=9789061323075.
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Kholtygin, A. F. "Modelling the induced clumping stochastic line profile variability." Universität Potsdam, 2007. http://opus.kobv.de/ubp/volltexte/2008/1818/.
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We model the line profile variability (lpv) in spectra of clumped stellar atmospheres using the Stochastic Clump Model (SCM) of the winds of early-type stars. In this model the formation of dense inhomogeneities (clumps) in the line driven winds is considered as being a stochastic process. It is supposed that the emission due to clumps mainly contributes to the intensities of emission lines in the stellar spectra. It is shown that in the framework of the SCM it is possible to reproduce both the mean line profiles and a common pattern of the lpv.
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Onof, Christian. "Stochastic modelling of British rainfall using Poisson processes." Thesis, Imperial College London, 1992. http://hdl.handle.net/10044/1/8718.
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Wang, Xi. "Smoothing with application to stochastic fire growth modelling." Thesis, University of British Columbia, 2017. http://hdl.handle.net/2429/62501.
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Modelling wildland fire spread stochastically is an important way to incorporate the uncertainty associated with this phenomenon. Fitting such a model to data from remote-sensed images could be used to provide accurate fire spread risk maps. We study a particular model from this perspective. One objective of this thesis is to verify the model on data collected under experimentally controlled conditions. We present the analysis of data from small-scale experimental fires that were digitally recorded. Data extraction and processing methods and issues are discussed, along with an estimation methodology. A critical part of the estimation methodology revolves around the smoothing of observed counts of burning and burnt out pixels as functions of elapsed time. We employ nonparametric regression for this purpose and consider two bias reduction strategies as possible ways to obtain more accurate estimates of the parameters underlying the stochastic fire spread model. An argument for partial validation of the model is also provided.Irving K. Barber School of Arts and Sciences (Okanagan)
Mathematics, Department of (Okanagan)
Graduate
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Lozano, Torrubia Pablo. "Stochastic modelling of abrasive waterjet controlled-depth machining." Thesis, University of Nottingham, 2016. http://eprints.nottingham.ac.uk/35119/.
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Abrasive micro-waterjet processing is a non-conventional machining method that can be used to manufacture complex shapes in difficult-to-cut materials. The constant development of new materials with enhanced properties has sparked the interest in alternative machining technologies. Among these non-conventional machining methods, Abrasive Waterjet Machining is regarded as a flexible technology with potential to cope with a wide range of materials and applications. The use of a soft tool (i.e. the jet) is very advantageous because it makes it possible to perform different operations without modifying the equipment. However, this advantage poses a significant challenge: the erosion power of the jet is controlled through a set of operating parameters, and it is therefore necessary to have a deep understanding of the relation between such parameters and the effect of the jet on the surface. The process itself is subject to strong random variations, and this makes it even more complex to develop a detailed understanding of the optimum strategies to control the jet. The main objective of this thesis is to develop mathematical frameworks that account for the stochastic nature of the process, and that have the capability to predict detailed statistical information of the eroded surfaces for different operating parameters. This is addressed with two modelling approaches: a finite element model where the system is regarded as a set of multiple particles hitting a workpiece at very high speed, and a geometrical model built on the idea of considering the abrasive waterjet as a generic energy beam and exploiting the geometrical properties of the system. In the Finite Element approach, a modelling framework with the capability of predicting the average shape of abrasive waterjet machined footprints and the variability along the trench has been developed for the first time. This is achieved by combining finite element analysis and Monte Carlo methods, and the model is validated at different feed speeds and tilt angles. The random nature of the system is included by considering the input parameters (i.e. size, relative orientation, or position within the jet of the abrasive particles) as random variables with associated probability distributions. The geometrical approach is a method to predict the variability of the jet footprint for different jet feed speeds. Since the objective is to incorporate the stochastic nature of the system in the model, a stochastic partial differential equation is used to describe the machined surface as the jet is moved over it. This framework is greatly advantageous because it can be used to make fast predictions of the variability of the trench profiles (to within < 8%), and it can therefore be implemented into CAD/CAM packages. The modelling work, focused on the understanding of how the operating parameters changes the effect of the jet on the surface, is accompanied by an experimental study to uncover how the material properties of the workpiece will affect the erosion process. This is carried out by machining trenches on model materials (i.e. materials with the same chemical composition, but different grain size), and performing and in-depth analysis of the material response, which shows how the machining process has a strong impact on the microstructure of the target material. The work developed in this thesis contributes to the understanding of the erosion process during abrasive waterjet machining and how stochastic methods can be used to enhance the current capabilities of this technology.
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Lim, Shen Hin Mechanical & Manufacturing Engineering Faculty of Engineering UNSW. "Calibration-free image sensor modelling: deterministic and stochastic." Awarded by:University of New South Wales. Mechanical & Manufacturing Engineering, 2009. http://handle.unsw.edu.au/1959.4/44563.
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This dissertation presents the calibration-free image sensor modelling process applicable for localisation, such that these are robust to changes in environment and in sensor properties. The modelling process consists of two distinct parts, which are deterministic and stochastic techniques, and is achieved using mechanistic deconvolution, where the sensor???s mechanical and electrical properties are utilised. In the deterministic technique, the sensor???s effective focal length is first estimated by known lens properties, and is used to approximate the lens system by a thick lens and its properties. The aperture stop position offset???which is one of the thick lens properties???then derives a new factor, namely calibration-free distortion effects factor, to characterise distortion effects inherent in the sensor. Using this factor and the given pan and tilt angles of an arbitrary plane of view, the corrected image data is generated. The corrected data complies with the image sensor constraints modified by the pan and tilt angles. In the stochastic technique, the stochastic focal length and distortion effects factor are first approximated, using tolerances of the mechanical and electrical properties. These are then utilised to develop the observation likelihood necessary in recursive Bayesian estimation. The proposed modelling process reduces dependency on image data, and, as a result, do not require experimental setup or calibration. An experimental setup was constructed to conduct extensive analysis on accuracy of the proposed modelling process and its robustness to changes in sensor properties and in pan and tilt angles without recalibration. This was compared with a conventional modelling process using three sensors with different specifications and achieved similar accuracy with one-seventh the number of iterations. The developed model has also shown itself to be robust and, in comparison to the conventional modelling process, reduced the errors by a factor of five. Using area coverage method and one-step lookahead as control strategies, the stochastic sensor model was applied into a recursive Bayesian estimation application and was also compared with a conventional approach. The proposed model provided better target estimation state, and also achieved higher efficiency and reliability when compared with the conventional approach.
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Cao, Robin [Verfasser]. "Hierarchical stochastic modelling in multistable perception / Robin Cao." Magdeburg : Universitätsbibliothek, 2017. http://d-nb.info/1138276545/34.
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Ferrero, Charlie David. "Stochastic modelling of thermal histories in sedimentary basins." Thesis, Imperial College London, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.408156.
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Blackwell, Paul Gavin. "The stochastic modelling of social and territorial behaviour." Thesis, University of Nottingham, 1990. http://eprints.nottingham.ac.uk/13594/.
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This thesis considers mathematical models of the interaction between social and territorial behaviour in animals, mainly by probabilistic methods. Chapter 1 introduces the Resource Dispersion Hypothesis, which suggests that territorial behaviour plus dispersed food resources can explain the existence of social groups, and describes an existing model of the process, due to Carr and Macdonald. In Chapter 2 the model of Carr and Macdonald is analysed, and in Chapter 3 an improved model is suggested and its main properties derived, primarily using renewal theory. Chapters 4 and 5 consider various spatial models for territory formation, and the effect, of spatial factors on social behaviour, using analytic and simulation-based methods. Chapter 6 considers the evolution of social behaviour using both discrete-time deterministic models and branching processes to investigate the viability of different strategies of social behaviour in the presence of dispersed resources.
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Zhang, Wenjuan. "Stochastic modelling and applications in condition-based maintenance." Thesis, University of Salford, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.409365.
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Keenan, Christopher Ryan. "Stochastic modelling for high fidelity DPGS quality assessment." Thesis, University College London (University of London), 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249721.
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