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Journal articles on the topic 'Stochastic parameters modelling'

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Author: Grafiati

Published: 30 May 2022

Last updated: 31 May 2022

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1

Beutler, G., A. Jäggi, U. Hugentobler, and L. Mervart. "Efficient satellite orbit modelling using pseudo-stochastic parameters." Journal of Geodesy 80, no. 7 (August 24, 2006): 353–72. http://dx.doi.org/10.1007/s00190-006-0072-6.

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2

Borzunov, S. V., M. E. Semenov, N. I. Sel’vesyuk, and P. A. Meleshenko. "Hysteretic Converters with Stochastic Parameters." Mathematical Models and Computer Simulations 12, no. 2 (March 2020): 164–75. http://dx.doi.org/10.1134/s2070048220020040.

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3

Ellam, L., M. Girolami, G. A. Pavliotis, and A. Wilson. "Stochastic modelling of urban structure." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2213 (May 2018): 20170700. http://dx.doi.org/10.1098/rspa.2017.0700.

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The building of mathematical and computer models of cities has a long history. The core elements are models of flows (spatial interaction) and the dynamics of structural evolution. In this article, we develop a stochastic model of urban structure to formally account for uncertainty arising from less predictable events. Standard practice has been to calibrate the spatial interaction models independently and to explore the dynamics through simulation. We present two significant results that will be transformative for both elements. First, we represent the structural variables through a single potential function and develop stochastic differential equations to model the evolution. Second, we show that the parameters of the spatial interaction model can be estimated from the structure alone, independently of flow data, using the Bayesian inferential framework. The posterior distribution is doubly intractable and poses significant computational challenges that we overcome using Markov chain Monte Carlo methods. We demonstrate our methodology with a case study on the London, UK, retail system.

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4

Marano, Giuseppe Carlo, Mariantonietta Morga, and Sara Sgobba. "Parameters Identification of Stochastic Nonstationary Process Used in Earthquake Modelling." International Journal of Geosciences 04, no. 02 (2013): 290–301. http://dx.doi.org/10.4236/ijg.2013.42027.

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5

Intsiful, Joseph, and Harald Kunstmann. "Upscaling of Land-Surface Parameters Through Inverse Stochastic SVAT-Modelling." Boundary-Layer Meteorology 129, no. 1 (September 13, 2008): 137–58. http://dx.doi.org/10.1007/s10546-008-9303-0.

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6

Dørum, C., O. S. Hopperstad, T. Berstad, and D. Dispinar. "Numerical modelling of magnesium die-castings using stochastic fracture parameters." Engineering Fracture Mechanics 76, no. 14 (September 2009): 2232–48. http://dx.doi.org/10.1016/j.engfracmech.2009.07.001.

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7

Frederiksen, Jorgen S., Terence J. O'Kane, and Meelis J. Zidikheri. "Subgrid modelling for geophysical flows." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1982 (January 13, 2013): 20120166. http://dx.doi.org/10.1098/rsta.2012.0166.

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Recently developed closure-based and stochastic model approaches to subgrid-scale modelling of eddy interactions are reviewed. It is shown how statistical dynamical closure models can be used to self-consistently calculate the eddy damping and stochastic backscatter parameters, required in large eddy simulations (LESs), from higher resolution simulations. A closely related direct stochastic modelling scheme that is more generally applicable to complex models is then described and applied to LESs of quasi-geostrophic turbulence of the atmosphere and oceans. The fundamental differences between atmospheric and oceanic LESs, which are related to the difference in the deformation scales in the two classes of flows, are discussed. It is noted that a stochastic approach may be crucial when baroclinic instability is inadequately resolved. Finally, inhomogeneous closure theory is applied to the complex problem of flow over topography; it is shown that it can be used to understand the successes and limitations of currently used heuristic schemes and to provide a basis for further developments in the future.

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8

Romansky, Radi. "Mathematical Modelling and Study of Stochastic Parameters of Computer Data Processing." Mathematics 9, no. 18 (September 12, 2021): 2240. http://dx.doi.org/10.3390/math9182240.

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The main goal of dispatching strategies is to minimize the total time for processing tasks at maximum performance of the computer system, which requires strict regulation of the workload of the processing units. To achieve this, it is necessary to conduct a preliminary study of the applied model for planning. The purpose of this article is to present an approach for automating the investigation and optimization of processes in a computer environment for task planning and processing. A stochastic input flow of incoming tasks for processing is considered and mathematical formalization of some probabilistic characteristics related to the complexity of its servicing has been made. On this basis, a software module by using program language APL2 has been developed to conduct experiments for analytical study and obtaining estimates of stochastic parameters of computer processing and dispatching. The proposed model is part of a generalized environment for program investigation of the computer processing organization and expands its field of application with additional research possibilities.

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9

Gassmann, H. I., and G. Infanger. "Modelling history-dependent parameters in the SMPS format for stochastic programming." IMA Journal of Management Mathematics 19, no. 1 (February 2, 2007): 87–97. http://dx.doi.org/10.1093/imaman/dpm006.

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10

ARTEMEV, S. S., and M. A. YAKUNIN. "Estimation of the parameters in stochastic differential equations." Russian Journal of Numerical Analysis and Mathematical Modelling 12, no. 1 (1997): 1–12. http://dx.doi.org/10.1515/rnam.1997.12.1.1.

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11

Korsunovs, Aleksandrs, Felician Campean, Gaurav Pant, Oscar Garcia-Afonso, and Efe Tunc. "Evaluation of zero-dimensional stochastic reactor modelling for a Diesel engine application." International Journal of Engine Research 21, no. 4 (April 29, 2019): 592–609. http://dx.doi.org/10.1177/1468087419845823.

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Prediction of engine-out emissions with high fidelity from in-cylinder combustion simulations is still a significant challenge early in the engine development process. This article contributes to this fast evolving body of knowledge by focusing on the evaluation of NO x emission prediction capability of a probability density function–based stochastic reactor engine models for a Diesel engine. The research implements a systematic approach to the study of the stochastic reactor engine model performance, underpinned by a detailed space-filling design of experiments (DoE)-based sensitivity analysis of both external and internal parameters, evaluating their effects on the accuracy in matching physical measurements of both in-cylinder conditions and NO x output. The approach proposed in this article introduces an automatic stochastic reactor engine model calibration methodology across the engine operating envelope, based on a multi-objective optimization approach. This aims to exploit opportunities for internal stochastic reactor engine model parameters tuning to achieve good overall modelling performance as a trade-off between physical in-cylinder measurements accuracy and the output NO x emission predictions error. The results from the case study provide a valuable insight into the effectiveness of the stochastic reactor engine model, showing good capability for NO x emissions prediction and trends, while pointing out the critical sensitivity to the external input parameters and modelling conditions.

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12

Christakos, George, and Dionissios T. Hristopulos. "Stochastic indicator analysis of contaminated sites." Journal of Applied Probability 34, no. 4 (December 1997): 988–1008. http://dx.doi.org/10.2307/3215012.

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We formulate stochastic indicator parameters that characterize pollution levels in geographical regions with heterogeneous contaminant distributions. The indicator parameters are expressed in terms of the random fields representing the contaminant distributions and the critical threshold level specified by health and environmental standards. Certain theoretical results are proven regarding univariate and bivariate indicator parameters. The analytical expressions obtained are general and can be used in practice for various types of contaminant distributions. A test of ergodicity-breaking is suggested for scientific and engineering applications in terms of the indicator parameters. Fractal characteristics of the indicator parameters are discussed. The effects of modelling and observation scale on exceedance contamination analysis are examined. Indicator random field parameters are studied on both continuum and lattice domains using analytical means and numerical simulations.

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13

Christakos, George, and Dionissios T. Hristopulos. "Stochastic indicator analysis of contaminated sites." Journal of Applied Probability 34, no. 04 (December 1997): 988–1008. http://dx.doi.org/10.1017/s0021900200101676.

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We formulate stochastic indicator parameters that characterize pollution levels in geographical regions with heterogeneous contaminant distributions. The indicator parameters are expressed in terms of the random fields representing the contaminant distributions and the critical threshold level specified by health and environmental standards. Certain theoretical results are proven regarding univariate and bivariate indicator parameters. The analytical expressions obtained are general and can be used in practice for various types of contaminant distributions. A test of ergodicity-breaking is suggested for scientific and engineering applications in terms of the indicator parameters. Fractal characteristics of the indicator parameters are discussed. The effects of modelling and observation scale on exceedance contamination analysis are examined. Indicator random field parameters are studied on both continuum and lattice domains using analytical means and numerical simulations.

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14

Rampino, Sergio, Mirco Zerbetto, and Antonino Polimeno. "Stochastic Modelling of 13C NMR Spin Relaxation Experiments in Oligosaccharides." Molecules 26, no. 9 (April 21, 2021): 2418. http://dx.doi.org/10.3390/molecules26092418.

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A framework for the stochastic description of relaxation processes in flexible macromolecules including dissipative effects has been recently introduced, starting from an atomistic view, describing the joint relaxation of internal coordinates and global degrees of freedom, and depending on parameters recoverable from classic force fields (energetics) and medium modelling at the continuum level (friction tensors). The new approach provides a rational context for the interpretation of magnetic resonance relaxation experiments. In its simplest formulation, the semi-flexible Brownian (SFB) model has been until now shown to reproduce correctly correlation functions and spectral densities related to orientational properties obtained by direct molecular dynamics simulations of peptides. Here, for the first time, we applied directly the SFB approach to the practical evaluation of high-quality 13C nuclear magnetic resonance relaxation parameters, T1 and T2, and the heteronuclear NOE of several oligosaccharides, which were previously interpreted on the basis of refined ad hoc modelling. The calculated NMR relaxation parameters were in agreement with the experimental data, showing that this general approach can be applied to diverse classes of molecular systems, with the minimal usage of adjustable parameters.

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15

Klimczak, Konrad, Piotr Oprocha, Jan Kusiak, Danuta Szeliga, Paweł Morkisz, Paweł Przybyłowicz, Natalia Czyżewska, and Maciej Pietrzyk. "Inverse Problem in Stochastic Approach to Modelling of Microstructural Parameters in Metallic Materials during Processing." Mathematical Problems in Engineering 2022 (April 12, 2022): 1–15. http://dx.doi.org/10.1155/2022/9690742.

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The need for a reliable prediction of the distribution of microstructural parameters in metallic materials during processing was the motivation for this work. The model describing the evolution of dislocation populations, which considers the stochastic aspects of occurring phenomena, was formulated. The validation of the presented model requires the application of proper parameters corresponding to the considered materials. These parameters have to be identified through the inverse analysis, which, on the other hand, uses optimization methods and requires the formulation of the appropriate objective function. In our case, where the model involves the stochastic parameters, it is a crucial task. Therefore, a specific form of the objective function for the inverse analysis was developed using a measure based on histograms. The elaborated original stochastic approach to modeling the phenomena occurring during the thermomechanical treatment of metals was validated on commercially pure copper and selected multiphase steel.

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16

Logan, L., V. Graham, and T. E. Unny. "Probability and stochastic modelling of water quality parameters in the Thames River." Canadian Journal of Civil Engineering 15, no. 3 (June 1, 1988): 430–36. http://dx.doi.org/10.1139/l88-058.

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Baseline information on water quality parameters is essential to the development of policies to manage and control con taminants in streams. Investigations on the probability behaviour of monthly statistical estimates reveal that the governing probability distributions are not fixed but change on a monthly basis; and they are non-Gaussian. Probability density functions are developed using a five-parameter polynomial density function, which allows successful preservation of the key moments of the baseline water quality sequence. Stochastic models for transformed series of concentration of total phosphorus and suspended solids are determined using the ARIMA process. Since the ARIMA family of processes requires that the underlying distributions for monthly events be Gaussian and time-invariant, appropriate transformations are made for mapping the monthly water quality data from its parent distribution to a N(0,1) distribution. The model constructed for the transformed monthly phosphorus variable is an ARIMA [1, 1, 0], while the transformed suspended solids series of monthly time step is adequately described using a white noise ARIMA model. The methodology developed provides a framework for modelling baseline water quality data at various tributaries. The transformations guarantee that the probability distribution of the observed series is incorporated into the model structure. Therefore, synthetic water quality series generated using these models reproduce the non-Gaussian time-varying probability distributions and maintain the serial relationship between consecutive monthly events. Key words: ARIMA process, non-Gaussian probability distribution, water quality time series, suspended solids data, phosphorus concentration series.

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17

Torrubia, P. Lozano, J. Billingham, and D. A. Axinte. "Stochastic simplified modelling of abrasive waterjet footprints." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2186 (February 2016): 20150836. http://dx.doi.org/10.1098/rspa.2015.0836.

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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. Predicting the effect of the jet on the surface for a given set of machine parameters is a key element of controlling the process. However, the noise of the process is significant, making it difficult to design reliable jet-path strategies that produce good quality parts via controlled-depth milling. The process is highly unstable and has a strong random component that can affect the quality of the workpiece, especially in the case of controlled-depth milling. This study describes a method to predict the variability of the jet footprint for different jet feed speeds. A stochastic partial differential equation is used to describe the etched surface as the jet is moved over it, assuming that the erosion process can be divided into two main components: a deterministic part that corresponds to the average erosion of the jet and a stochastic part that accounts for the noise generated at different stages of the process. The model predicts the variability of the trench profiles to within less than 8%. These advances could enable abrasive micro-waterjet technology to be a suitable technology for controlled-depth milling.

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18

Figoń, Piotr. "Application of parametric modelling methods for estimating the parameters of damped sinusoidal signals." Bulletin of the Military University of Technology 66, no. 4 (December 31, 2017): 193–208. http://dx.doi.org/10.5604/01.3001.0010.8331.

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The paper describes the results of analyses aimed at obtaining information on selected parameters of the deterministic component of a signal being the sum of two waveforms, an exponentially damped sinusoidal waveform and a stochastic waveform. Keywords: linear prediction, optimisation, analytical signal

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19

Chia, Min Yan, Yuk Feng Huang, Chai Hoon Koo, and Zheng Rong Chong. "Long-term forecasting of climatic parameters using parametric and non-parametric stochastic modelling." E3S Web of Conferences 347 (2022): 05013. http://dx.doi.org/10.1051/e3sconf/202234705013.

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Climatic parameters fluctuate dynamically and their turbulences become more significant as the influence of the climate change increases. A robust model that is able to factor in the recent climate change for long-term climatic parameters forecasting is desired to strategically plan for future anthropogenic activities. In this study, two stochastic time series model, namely the seasonal auto-regressive integrated moving average (SARIMA) model and the artificial neural network (ANN) model are used to predict monthly mean temperature (Tmean), relative humidity (RH), wind speed (u) and pan evaporation (Epan) up to 12 months ahead. This study is conducted using data collected from three meteorological stations in the northern region of the Peninsular Malaysia. The stochastic models forecasted the Tmean with the highest accuracy, followed by RH, u and Epan. Besides, despite the increasing time step (from 1 to 12 months), the accuracy of the models remain consistent. However, both of the models are susceptible to the occurrence of extreme climates. In general, the SARIMA model performs better than the ANN model, probably attributed to its ability to consider the seasonality of the climatic data rather than depending solely on black-box computation.

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20

Quetting, Florian, Pavel Hora, and Karl Roll. "Modelling of Strain Hardening Behaviour of Sheet Metals for Stochastic Simulations." Key Engineering Materials 504-506 (February 2012): 41–46. http://dx.doi.org/10.4028/www.scientific.net/kem.504-506.41.

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In current forming simulations, Ghosh or Hockett-Sherby extrapolation functions are used to model strain hardening effects of sheet metals. When it comes to stochastic simulations, the respective parameters have to be recalculated according to the scattering of the mechanical material properties like yield or tensile strength. As present stochastic samplings for deep drawing simulations only consider yield strength and tensile strength, it is non-trivial securing the extrapolated area of strain hardening curves due to lack of data beyond uniform strain. It is current practice to improve the description of the flow curve beyond uniform elongation point by using the maximum force criterion, which takes into account the gradient of the yield curve at the last known point. The corresponding system of equations has to be solved numerically. We propose a method for adjusting parameters of the Ghosh or Hockett-Sherby extrapolation functions, which overcomes the need of numerical calculations and keeps flow curve information from the extrapolated interval, even if the stochastic sampling doesn’t incorporate any data regarding that area.

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21

Gao, Jiti. "Modelling long-range-dependent Gaussian processes with application in continuous-time financial models." Journal of Applied Probability 41, no. 02 (June 2004): 467–82. http://dx.doi.org/10.1017/s0021900200014431.

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This paper considers a class of continuous-time long-range-dependent Gaussian processes. The corresponding spectral density is assumed to have a general and flexible form, which covers some important and special cases. For example, the spectral density of a continuous-time fractional stochastic differential equation is included. A modelling procedure is then established through estimating the parameters involved in the spectral density by using an extended continuous-time version of the Gauss–Whittle objective function. The resulting estimates are shown to be strongly consistent and asymptotically normal. An application of the modelling procedure to the identification and modelling of a fractional stochastic volatility is discussed in some detail.

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Gao, Jiti. "Modelling long-range-dependent Gaussian processes with application in continuous-time financial models." Journal of Applied Probability 41, no. 2 (June 2004): 467–82. http://dx.doi.org/10.1239/jap/1082999079.

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This paper considers a class of continuous-time long-range-dependent Gaussian processes. The corresponding spectral density is assumed to have a general and flexible form, which covers some important and special cases. For example, the spectral density of a continuous-time fractional stochastic differential equation is included. A modelling procedure is then established through estimating the parameters involved in the spectral density by using an extended continuous-time version of the Gauss–Whittle objective function. The resulting estimates are shown to be strongly consistent and asymptotically normal. An application of the modelling procedure to the identification and modelling of a fractional stochastic volatility is discussed in some detail.

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23

Shi, Peiming, Pei Li, Shujun An, and Dongying Han. "Stochastic Resonance in a Multistable System Driven by Gaussian Noise." Discrete Dynamics in Nature and Society 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/1093562.

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Stochastic resonance (SR) is investigated in a multistable system driven by Gaussian white noise. Using adiabatic elimination theory and three-state theory, the signal-to-noise ratio (SNR) is derived. We find the effects of the noise intensity and the resonance system parametersb,c, anddon the SNR; the results show that SNR is a nonmonotonic function of the noise intensity; therefore, a multistable SR is found in this system, and the value of the peak changes with changing the system parameters.

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24

Jimoh, O. D., and P. Webster. "Stochastic modelling of daily rainfall in Nigeria: intra-annual variation of model parameters." Journal of Hydrology 222, no. 1-4 (September 1999): 1–17. http://dx.doi.org/10.1016/s0022-1694(99)00088-8.

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25

Capasso, V., and C. Salani. "Stochastic birth-and-growth processes modelling crystallization of polymers with spatially heterogeneous parameters." Nonlinear Analysis: Real World Applications 1, no. 4 (December 2000): 485–98. http://dx.doi.org/10.1016/s0362-546x(99)00289-8.

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26

Jurecka, Stanislav, and Jarmila Mullerova. "Thin Film Optical Parameters Determination by the Dynamical Modelling and Stochastic Optimization Method." Communications - Scientific letters of the University of Zilina 8, no. 1 (March 31, 2006): 22–24. http://dx.doi.org/10.26552/com.c.2006.1.22-24.

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27

Zabulionis, Darius, Ona Lukoševičienė, Rimantas Kačianauskas, Liudas Tumonis, and Romualdas Kliukas. "Stochastic Lattice Modelling of the Force-Displacement and Cracking Behaviour of the Steel Reinforced Tie." Mathematical Problems in Engineering 2019 (April 10, 2019): 1–17. http://dx.doi.org/10.1155/2019/6340656.

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The stochastic modelling of the microcracking and the force-displacement behaviour of the tensile steel reinforced tie using the lattice model is presented in the current article. The three-dimension problem of the modelling of the tie is reduced to the two-dimensional so as the main stiffness parameters of the concrete and the reinforcement of the two-dimensional model would be the same as for the three-dimensional. The concrete and steel obey the Hook law. All elastic constants, as well as dimensions of the tie, were assumed as the deterministic quantities except for the critical concrete tensile strains which were treated as a two-dimensional stationary uncorrelated truncated Gaussian random field. The discrete element approach and the explicit integration scheme have been used for the modelling. The estimations of the main parameters of the force-displacement behaviour stochastic process and other statistical indexes were obtained using 72 realization of the force-displacement behaviour of a chosen model. Extra two stochastic realizations of the two different models, as well as three deterministic models, were modelled to compare stochastic and deterministic behaviour of the force-displacement behaviour. The analysis showed that the force-displacement behaviour of the tie under tensile force cannot be treated as a Gaussian stochastic process when the p value is 0.05 at the small displacements and within the interval when the cracking of the concrete is very intensive. However, at the bigger displacements, when the cracking becomes less intensive, the tensile force can be treated as a Gaussian random variable.

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Hurn, A. S., and K. A. Lindsay. "Estimating the parameters of stochastic differential equations." Mathematics and Computers in Simulation 48, no. 4-6 (June 1999): 373–84. http://dx.doi.org/10.1016/s0378-4754(99)00017-8.

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Jacobsen, J. L., H. Madsen, and P. Harremoès. "A stochastic model for two-station hydraulics exhibiting transient impact." Water Science and Technology 36, no. 5 (September 1, 1997): 19–26. http://dx.doi.org/10.2166/wst.1997.0156.

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The objective of the paper is to interpret data on water level variation in a river affected by overflow from a sewer system during rain. The simplest possible, hydraulic description is combined with stochastic methods for data analysis and model parameter estimation. This combination of deterministic and stochastic interpretation is called grey box modelling. As a deterministic description the linear reservoir approximation is used. A series of linear reservoirs in sufficient number will approximate a plug flow reactor. The choice of number is an empirical expression of the longitudinal dispersion in the river. This approximation is expected to be a sufficiently good approximation as a tool for the ultimate aim: the description of pollutant transport in the river. The grey box modelling involves a statistical tool for estimation of the parameters in the deterministic model. The advantage is that the parameters have physical meaning, as opposed to many other statistically estimated, empirical parameters. The identifiability of each parameter, the uncertainty of the parameter estimation and the overall uncertainty of the simulation are determined.

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30

Meng, Xiangsong, and Lixing Yang. "Stochastic Portfolio Selection Problem with Reliability Criteria." Discrete Dynamics in Nature and Society 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/8417643.

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Portfolio selection focuses on allocating the capital to a set of securities such that the profit or the risks can be optimized. Due to the uncertainty of the real-world life, the return parameters always take uncertain information in the realistic environments because of the scarcity of the a priori knowledge or uncertain disturbances. This paper particularly considers a portfolio selection process in the stochastic environment, where the return parameters are characterized by sample-based correlated random variables. To decrease the decision risks, three evaluation criteria are proposed to generate the reliable portfolio selection plans, including max-min reliability criterion, percentile reliability criterion, and expected disutility criterion. The equivalent linear (mixed integer) programming models are also deduced for different evaluation strategies. A genetic algorithm with a polishing strategy is designed to search for the approximate optimal solutions of the proposed models. Finally, a series of numerical experiments are implemented to demonstrate the effectiveness and performance of the proposed approaches.

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Narayana, C., B. Mahaboob, B. Venkateswarlu, J. Ravi sankar, and P. Balasiddamuni. "A Treatise on Testing General Linear Hypothesis in Stochastic Linear Regression Model." International Journal of Engineering & Technology 7, no. 4.10 (October 2, 2018): 539. http://dx.doi.org/10.14419/ijet.v7i4.10.21223.

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The main objective of this research article is to propose test statistics for testing general linear hypothesis about parameters in stochastics linear regression model using studentized residuals, RLS estimates and unrestricted internally studentized residuals. In 1998, M. Celia Rodriguez -Campos et.al [1] introduced a new test statistics to test the hypothesis of a generalized linear model in a regression context with random design. Li Cai et.al [2] provide a new test statistic for testing linear hypothesis in an OLS regression model that not assume homoscedasticity. P. Balasiddamuni et.al [3] proposed some advanced tools for mathematical and stochastical modelling.

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32

Baili, Hana. "Hybrid stochastic differential systems in pharmacokinetics." IMA Journal of Mathematical Control and Information 39, no. 1 (December 7, 2021): 22–59. http://dx.doi.org/10.1093/imamci/dnab034.

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Abstract Modelling patient medication poor compliance combined with the inherent uncertainty in a bioavailability trial leads recognizably to the fact that plasma concentration-time curve must be treated as a random process. We suggest for modelling a general class of hybrid stochastic differential systems (HSDS). Roughly speaking, a HSDS is a piecewise diffusion process with jumps of two types: spontaneous and predictable. The essential tasks for us afterwards are to identify the model ingredients and to derive its bearings; of interest are a couple of operators associated to every Markov process: the generating operator and the Fokker–Planck operator. The model induces a Fokker–Planck–Kolmogorov equation along with moment equations, and computations based on direct solutions of the latter make it possible to study the variability of the concentration around its mean as compared to the full compliance case and to assess the effect of some parameters such as the intake and elimination rates.

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33

Molostvov, Vitaly. "Multiple criteria optimization for stochastic systems with uncertain parameters." Model Assisted Statistics and Applications 6, no. 3 (August 26, 2011): 231–37. http://dx.doi.org/10.3233/mas-2011-0205.

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34

Liao, Shuohao, Tomáš Vejchodský, and Radek Erban. "Tensor methods for parameter estimation and bifurcation analysis of stochastic reaction networks." Journal of The Royal Society Interface 12, no. 108 (July 2015): 20150233. http://dx.doi.org/10.1098/rsif.2015.0233.

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Stochastic modelling of gene regulatory networks provides an indispensable tool for understanding how random events at the molecular level influence cellular functions. A common challenge of stochastic models is to calibrate a large number of model parameters against the experimental data. Another difficulty is to study how the behaviour of a stochastic model depends on its parameters, i.e. whether a change in model parameters can lead to a significant qualitative change in model behaviour (bifurcation). In this paper, tensor-structured parametric analysis (TPA) is developed to address these computational challenges. It is based on recently proposed low-parametric tensor-structured representations of classical matrices and vectors. This approach enables simultaneous computation of the model properties for all parameter values within a parameter space. The TPA is illustrated by studying the parameter estimation, robustness, sensitivity and bifurcation structure in stochastic models of biochemical networks. A Matlab implementation of the TPA is available at http://www.stobifan.org .

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35

Kong, Weili, and Yuanfu Shao. "Stochastic Periodic Solution and Persistence of a Nonautonomous Impulsive System with Nonlinear Self-Interaction." Discrete Dynamics in Nature and Society 2020 (February 10, 2020): 1–19. http://dx.doi.org/10.1155/2020/1053401.

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Considering periodic environmental changes and random disturbance, we explore the dynamical behaviors of a stochastic competitive system with impulsive and periodic parameters in this paper. Firstly, by use of extreme-value theory of quadratic function and constructing suitable functional, we study the existence of periodic Markovian process. Secondly, by comparison theory of the stochastic differential equation, we study the extinction and permanence in the mean of all species. Thirdly, applying an important lemma, we investigate the stochastic persistence of this system. Finally, some numerical simulations are given to illustrate the main results.

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Paszkiewicz, Bartlomiej K., Bogdan Paszkiewicz, and Andrzej Dziedzic. "Fabrication Process Stochastic Model for Yield Estimation in Microwave Semiconductor Devices Production." Journal of Engineering 2022 (April 29, 2022): 1–7. http://dx.doi.org/10.1155/2022/5561059.

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This paper presents a new methodology for simulation of production processes in order to determine device parametric yield. The elaborated methodology is focused on capturing stochastic relations between every parameter of the subsequent processes that are impossible to determine directly. The current state-of-the-art together with the gaps in the knowledge regarding yield modelling is presented. A novel approach to the important issue of effective yield modelling that allows the overcoming of current challenges is presented. The methodology’s usefulness is validated with the example of the fabrication process of AlGaN/GaN HEMT (high electron mobility transistor) for application in high-frequency electronics. Fabrication of AlGaN/GaN HEMTs is a complex process due to the large number of technological stages required, most of which are still the subject of ongoing research. Most importantly, the approach presented in this paper could be easily applied to the modelling of any complex production process in every case where it is necessary to examine relations between the final product parameters distribution and the values of the involved process parameters.

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Plessis, Jacques L. du, and Heinz E. Jacobs. "Procedure to Derive Parameters for Stochastic Modelling of Outdoor Water use in Residential Estates." Procedia Engineering 119 (2015): 803–12. http://dx.doi.org/10.1016/j.proeng.2015.08.942.

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Kunstmann, Harald. "Effective SVAT-model parameters through inverse stochastic modelling and second-order first moment propagation." Journal of Hydrology 348, no. 1-2 (January 2008): 13–26. http://dx.doi.org/10.1016/j.jhydrol.2007.09.032.

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Benedek, Kálmán, and Gyula Dankó. "Stochastic hydrogeological modelling of fractured rocks: a generic case study in the Mórágy Granite Formation (South Hungary)." Geologica Carpathica 60, no. 4 (August 1, 2009): 271–81. http://dx.doi.org/10.2478/v10096-009-0019-y.

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Stochastic hydrogeological modelling of fractured rocks: a generic case study in the Mórágy Granite Formation (South Hungary)In connection with the Hungarian radioactive waste disposal program a detailed study of the mass properties of the potential host rock (granite) has been carried out. Using the results of this study the various parameters (orientation, length, intensity, transmissivity, etc.) describing a fracture set were estimated on the basis of statistical considerations. These estimates served as basic input parameters for stochastic hydrogeological modelling of discrete fracture networks (DFN), which is a strongly developing area of hydrology, providing geologically realistic geometry for site investigations. The synthetic fracture systems generated were tested against some (but not all) field observations. The models built up on the basis of the statistical descriptions showed the same equivalent hydraulic conductivity for the modelled region as the field measurements. In addition, the models reproduce the observed hydraulic head-scattering along vertical boreholes. On the basis of the stochastic simulations of the fracture system some input parameters for the performance assessment of the planned repository were investigated. Calculation of flows into a planned disposal tunnel indicated that if the hydraulic conductivity of the material in the tunnel is the only variable parameter then there are two thresholds: under 1×10-9m/s and above 1×10-5m/s further change of the hydraulic conductivity does not dramatically affect the inflow.

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Salarieh, Hassan, and Aria Alasty. "Adaptive synchronization of two chaotic systems with stochastic unknown parameters." Communications in Nonlinear Science and Numerical Simulation 14, no. 2 (February 2009): 508–19. http://dx.doi.org/10.1016/j.cnsns.2007.09.002.

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Whelan, M. J., E. G. Hope, and K. Fox. "Stochastic modelling of phosphorus transfers from agricultural land to aquatic ecosystems." Water Science and Technology 45, no. 9 (May 1, 2002): 167–76. http://dx.doi.org/10.2166/wst.2002.0231.

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This paper describes a simple model of phosphorus (P) transfer from agricultural land to surface waters which incorporates the effects of spatial variability in catchment properties and uncertainty in model parameter values. TOPMODEL concepts are used to estimate water, solute and sediment fluxes to water bodies. The model predicts the spatial distribution of water table depth and saturation-excess overland flow based on topography. Dissolved P (DP) transfer is assumed to occur vertically in the unsaturated zone and laterally in the saturated zone. Readily soluble P is assumed to decrease exponentially with soil depth. Particulate P (PP) transfers are modelled by estimating overland flow discharge and associated sediment transport capacity. Uncertainty in the distribution of soil surface P concentrations and model parameters controlling the mobility of soil P are incorporated using Monte Carlo simulation. Predicted losses of DP are well correlated with discharge and those of PP are episodic. Highest losses of P tended to be predicted near to the stream where the water table is close to the surface. The combination of a deterministic model core with a stochastic generation of model parameters or state variables provides an attractive way of embracing variability and uncertainty in models of this kind.

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Lewy, P., and A. Nielsen. "Modelling stochastic fish stock dynamics using Markov Chain Monte Carlo." ICES Journal of Marine Science 60, no. 4 (January 1, 2003): 743–52. http://dx.doi.org/10.1016/s1054-3139(03)00080-8.

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Abstract A new age-structured stock dynamics approach including stochastic survival and recruitment processes is developed and implemented. The model is able to analyse detailed sources of information used in standard age-based fish stock assessment such as catch-at-age and effort data from commercial fleets and research surveys. The stock numbers are treated as unobserved variables subject to process errors while the catches are observed variables subject to both sampling and process errors. Results obtained for North Sea plaice using Markov Chain Monte Carlo methods indicate that the process error by far accounts for most of the variation compared to sampling error. Comparison with results from a simpler separable model indicates that the new model provides more precise estimates with fewer parameters.

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V. Poliarus, O., Y. O. Poliakov, I. L. Nazarenko, Y. T. Borovyk, and M. V. Kondratiuk. "Detection of Jumps Parameters in Economic Processes(the Case of Modelling Profitability)." International Journal of Engineering & Technology 7, no. 4.3 (September 15, 2018): 488. http://dx.doi.org/10.14419/ijet.v7i4.3.19922.

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A new method of parameters jumps detection in economic processes is presented. A jump of the economic process parameter must be understood as a rapid parameter change for a time that does not exceed the period of process registration. A system of stochastic differential equations for a posteriori density probability of a jump is synthesized. The solution of the system is the probability of a parameter jump, the estimation and variance of the jump in the presence of a priori information under conditions of noise influence. The simulation results are conducted for profitability of machine building industry of Kharkiv region, Ukraine. The system provides detection of jump parameters, even in conditions of intense noise of economic nature. To increase the probability of finding jumps it is necessary to have a priori information.

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ANISHCHENKO, V. S., M. A. SAFONOVA, and L. O. CHUA. "STOCHASTIC RESONANCE IN CHUA’S CIRCUIT." International Journal of Bifurcation and Chaos 02, no. 02 (June 1992): 397–401. http://dx.doi.org/10.1142/s0218127492000379.

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In this paper, we report numerical observations of the stochastic resonance (SR) phenomenon in a bistable chaotic electronic circuit (namely, Chua’s circuit) driven simultaneously by noise and a sinusoidal signal. It is shown that the noise-induced “chaos-chaos” type intermittency is a physical mechanism of the SR-phenomenon in chaotic systems. The resulting amplification of the sinusoidal signal intensity is due to a coherent interaction of three characteristic frequencies of the system. The SR-phenomenon can be controlled by a variation of either the noise intensity or the system parameters in the absence of noise.

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Şahin, Y. Ş., and S. Levitan. "A stochastic investment model for actuarial use in South Africa." South African Actuarial Journal 20, no. 1 (January 28, 2021): 49–79. http://dx.doi.org/10.4314/saaj.v20i1.3.

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In this paper, we propose a stochastic investment model for actuarial use in South Africa by modelling price inflation rates, share dividends, long-term and short-term interest rates for the period 1960–2018 and inflation-linked bonds for the period 2000–2018. Possible bi-directional relations between the economic series have been considered, the parameters and their confidence intervals have been estimated recursively to examine their stability, and the model validation has been tested. The model is designed to provide long-term forecasts that should find application in long-term modelling for institutions such as pension funds and life insurance companies in South Africa Keywords: Stochastic investment models; price inflation; share dividend yields; share dividends; share prices; long-term interest rates; short-term interest rates; inflation-linked bonds; South Africa

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Ahmed, Mohamed A., Talal M. Alkhamis, and Douglas R. Miller. "Time-inhomogeneous discrete stochastic search methods for optimal Bernoulli parameters." Applied Stochastic Models and Data Analysis 14, no. 3 (September 1998): 199–217. http://dx.doi.org/10.1002/(sici)1099-0747(199809)14:3<199::aid-asm348>3.0.co;2-3.

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Hauseux, Paul, Jack S. Hale, Stéphane Cotin, and Stéphane P. A. Bordas. "Quantifying the uncertainty in a hyperelastic soft tissue model with stochastic parameters." Applied Mathematical Modelling 62 (October 2018): 86–102. http://dx.doi.org/10.1016/j.apm.2018.04.021.

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Deogekar, S., M. R. Islam, and R. C. Picu. "Parameters controlling the strength of stochastic fibrous materials." International Journal of Solids and Structures 168 (August 2019): 194–202. http://dx.doi.org/10.1016/j.ijsolstr.2019.03.033.

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Klein, Olaf, Daniele Davino, and Ciro Visone. "On forward and inverse uncertainty quantification for models involving hysteresis operators." Mathematical Modelling of Natural Phenomena 15 (2020): 53. http://dx.doi.org/10.1051/mmnp/2020009.

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Parameters within hysteresis operators modeling real world objects have to be identified from measurements and are therefore subject to corresponding errors. To investigate the influence of these errors, the methods of Uncertainty Quantification (UQ) are applied. Results of forward UQ for a play operator with a stochastic yield limit are presented. Moreover, inverse UQ is performed to identify the parameters in the weight function in a Prandtl-Ishlinskiĭ operator and the uncertainties of these parameters.

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Zhu, Quanxin, and Jinde Cao. "Stochastic Stability of Neural Networks with Both Markovian Jump Parameters and Continuously Distributed Delays." Discrete Dynamics in Nature and Society 2009 (2009): 1–20. http://dx.doi.org/10.1155/2009/490515.

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The problem of stochastic stability is investigated for a class of neural networks with both Markovian jump parameters and continuously distributed delays. The jumping parameters are modeled as a continuous-time, finite-state Markov chain. By constructing appropriate Lyapunov-Krasovskii functionals, some novel stability conditions are obtained in terms of linear matrix inequalities (LMIs). The proposed LMI-based criteria are computationally efficient as they can be easily checked by using recently developed algorithms in solving LMIs. A numerical example is provided to show the effectiveness of the theoretical results and demonstrate the LMI criteria existed in the earlier literature fail. The results obtained in this paper improve and generalize those given in the previous literature.

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