Academic literature on the topic 'Stochastic second order methods'
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Journal articles on the topic "Stochastic second order methods":
Burrage, Kevin, Ian Lenane, and Grant Lythe. "Numerical Methods for Second‐Order Stochastic Differential Equations." SIAM Journal on Scientific Computing 29, no. 1 (January 2007): 245–64. http://dx.doi.org/10.1137/050646032.
Tocino, A., and J. Vigo-Aguiar. "Weak Second Order Conditions for Stochastic Runge--Kutta Methods." SIAM Journal on Scientific Computing 24, no. 2 (January 2002): 507–23. http://dx.doi.org/10.1137/s1064827501387814.
Komori, Yoshio. "Weak second-order stochastic Runge–Kutta methods for non-commutative stochastic differential equations." Journal of Computational and Applied Mathematics 206, no. 1 (September 2007): 158–73. http://dx.doi.org/10.1016/j.cam.2006.06.006.
Tang, Xiao, and Aiguo Xiao. "Efficient weak second-order stochastic Runge–Kutta methods for Itô stochastic differential equations." BIT Numerical Mathematics 57, no. 1 (April 26, 2016): 241–60. http://dx.doi.org/10.1007/s10543-016-0618-9.
Moxnes, John F., and Kjell Hausken. "Introducing Randomness into First-Order and Second-Order Deterministic Differential Equations." Advances in Mathematical Physics 2010 (2010): 1–42. http://dx.doi.org/10.1155/2010/509326.
Rößler, Andreas. "Second Order Runge–Kutta Methods for Itô Stochastic Differential Equations." SIAM Journal on Numerical Analysis 47, no. 3 (January 2009): 1713–38. http://dx.doi.org/10.1137/060673308.
Rößler, Andreas. "Second order Runge–Kutta methods for Stratonovich stochastic differential equations." BIT Numerical Mathematics 47, no. 3 (May 12, 2007): 657–80. http://dx.doi.org/10.1007/s10543-007-0130-3.
Wang, Xiao, and Hongchao Zhang. "Inexact proximal stochastic second-order methods for nonconvex composite optimization." Optimization Methods and Software 35, no. 4 (January 15, 2020): 808–35. http://dx.doi.org/10.1080/10556788.2020.1713128.
Abdulle, Assyr, Gilles Vilmart, and Konstantinos C. Zygalakis. "Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations." SIAM Journal on Scientific Computing 35, no. 4 (January 2013): A1792—A1814. http://dx.doi.org/10.1137/12088954x.
Komori, Yoshio, and Kevin Burrage. "Weak second order S-ROCK methods for Stratonovich stochastic differential equations." Journal of Computational and Applied Mathematics 236, no. 11 (May 2012): 2895–908. http://dx.doi.org/10.1016/j.cam.2012.01.033.
Dissertations / Theses on the topic "Stochastic second order methods":
Yuan, Rui. "Stochastic Second Order Methods and Finite Time Analysis of Policy Gradient Methods." Electronic Thesis or Diss., Institut polytechnique de Paris, 2023. http://www.theses.fr/2023IPPAT010.
To solve large scale machine learning problems, first-order methods such as stochastic gradient descent and ADAM are the methods of choice because of their low cost per iteration. The issue with first order methods is that they can require extensive parameter tuning, and/or knowledge of the parameters of the problem. There is now a concerted effort to develop efficient stochastic second order methods to solve large scale machine learning problems. The motivation is that they require less parameter tuning and converge for wider variety of models and datasets. In the first part of the thesis, we presented a principled approach for designing stochastic Newton methods for solving both nonlinear equations and optimization problems in an efficient manner. Our approach has two steps. First, we can re-write the nonlinear equations or the optimization problem as desired nonlinear equations. Second, we apply new stochastic second order methods to solve this system of nonlinear equations. Through our general approach, we showcase many specific new second-order algorithms that can solve the large machine learning problems efficiently without requiring knowledge of the problem nor parameter tuning. In the second part of the thesis, we then focus on optimization algorithms applied in a specific domain: reinforcement learning (RL). This part is independent to the first part of the thesis. To achieve such high performance of RL problems, policy gradient (PG) and its variant, natural policy gradient (NPG), are the foundations of the several state of the art algorithms (e.g., TRPO and PPO) used in deep RL. In spite of the empirical success of RL and PG methods, a solid theoretical understanding of even the “vanilla” PG has long been elusive. By leveraging the RL structure of the problem together with modern optimization proof techniques, we derive new finite time analysis of both PG and NPG. Through our analysis, we also bring new insights to the methods with better hyperparameter choices
Auffredic, Jérémy. "A second order Runge–Kutta method for the Gatheral model." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-49170.
Cheng, Jianqiang. "Stochastic Combinatorial Optimization." Thesis, Paris 11, 2013. http://www.theses.fr/2013PA112261.
In this thesis, we studied three types of stochastic problems: chance constrained problems, distributionally robust problems as well as the simple recourse problems. For the stochastic programming problems, there are two main difficulties. One is that feasible sets of stochastic problems is not convex in general. The other main challenge arises from the need to calculate conditional expectation or probability both of which are involving multi-dimensional integrations. Due to the two major difficulties, for all three studied problems, we solved them with approximation approaches.We first study two types of chance constrained problems: linear program with joint chance constraints problem (LPPC) as well as maximum probability problem (MPP). For both problems, we assume that the random matrix is normally distributed and its vector rows are independent. We first dealt with LPPC which is generally not convex. We approximate it with two second-order cone programming (SOCP) problems. Furthermore under mild conditions, the optimal values of the two SOCP problems are a lower and upper bounds of the original problem respectively. For the second problem, we studied a variant of stochastic resource constrained shortest path problem (called SRCSP for short), which is to maximize probability of resource constraints. To solve the problem, we proposed to use a branch-and-bound framework to come up with the optimal solution. As its corresponding linear relaxation is generally not convex, we give a convex approximation. Finally, numerical tests on the random instances were conducted for both problems. With respect to LPPC, the numerical results showed that the approach we proposed outperforms Bonferroni and Jagannathan approximations. While for the MPP, the numerical results on generated instances substantiated that the convex approximation outperforms the individual approximation method.Then we study a distributionally robust stochastic quadratic knapsack problems, where we only know part of information about the random variables, such as its first and second moments. We proved that the single knapsack problem (SKP) is a semedefinite problem (SDP) after applying the SDP relaxation scheme to the binary constraints. Despite the fact that it is not the case for the multidimensional knapsack problem (MKP), two good approximations of the relaxed version of the problem are provided which obtain upper and lower bounds that appear numerically close to each other for a range of problem instances. Our numerical experiments also indicated that our proposed lower bounding approximation outperforms the approximations that are based on Bonferroni's inequality and the work by Zymler et al.. Besides, an extensive set of experiments were conducted to illustrate how the conservativeness of the robust solutions does pay off in terms of ensuring the chance constraint is satisfied (or nearly satisfied) under a wide range of distribution fluctuations. Moreover, our approach can be applied to a large number of stochastic optimization problems with binary variables.Finally, a stochastic version of the shortest path problem is studied. We proved that in some cases the stochastic shortest path problem can be greatly simplified by reformulating it as the classic shortest path problem, which can be solved in polynomial time. To solve the general problem, we proposed to use a branch-and-bound framework to search the set of feasible paths. Lower bounds are obtained by solving the corresponding linear relaxation which in turn is done using a Stochastic Projected Gradient algorithm involving an active set method. Meanwhile, numerical examples were conducted to illustrate the effectiveness of the obtained algorithm. Concerning the resolution of the continuous relaxation, our Stochastic Projected Gradient algorithm clearly outperforms Matlab optimization toolbox on large graphs
Sabbagh, Wissal. "Some Contributions on Probabilistic Interpretation For Nonlinear Stochastic PDEs." Thesis, Le Mans, 2014. http://www.theses.fr/2014LEMA1019/document.
The objective of this thesis is to study the probabilistic representation (Feynman-Kac for- mula) of different classes ofStochastic Nonlinear PDEs (semilinear, fully nonlinear, reflected in a domain) by means of backward doubly stochastic differential equations (BDSDEs). This thesis contains four different parts. We deal in the first part with the second order BDS- DEs (2BDSDEs). We show the existence and uniqueness of solutions of 2BDSDEs using quasi sure stochastic control technics. The main motivation of this study is the probabilistic representation for solution of fully nonlinear SPDEs. First, under regularity assumptions on the coefficients, we give a Feynman-Kac formula for classical solution of fully nonlinear SPDEs and we generalize the work of Soner, Touzi and Zhang (2010-2012) for deterministic fully nonlinear PDE. Then, under weaker assumptions on the coefficients, we prove the probabilistic representation for stochastic viscosity solution of fully nonlinear SPDEs. In the second part, we study the Sobolev solution of obstacle problem for partial integro-differentialequations (PIDEs). Specifically, we show the Feynman-Kac formula for PIDEs via reflected backward stochastic differentialequations with jumps (BSDEs). Specifically, we establish the existence and uniqueness of the solution of the obstacle problem, which is regarded as a pair consisting of the solution and the measure of reflection. The approach is based on stochastic flow technics developed in Bally and Matoussi (2001) but the proofs are more technical. In the third part, we discuss the existence and uniqueness for RBDSDEs in a convex domain D without any regularity condition on the boundary. In addition, using the approach based on the technics of stochastic flow we provide the probabilistic interpretation of Sobolev solution of a class of reflected SPDEs in a convex domain via RBDSDEs. Finally, we are interested in the numerical solution of BDSDEs with random terminal time. The main motivation is to give a probabilistic representation of Sobolev solution of semilinear SPDEs with Dirichlet null condition. In this part, we study the strong approximation of this class of BDSDEs when the random terminal time is the first exit time of an SDE from a cylindrical domain. Thus, we give bounds for the discrete-time approximation error.. We conclude this part with numerical tests showing that this approach is effective
El-Sharif, Najla Saleh Ahmed. "Second-order methods for some nonlinear second-order initial-value problems with forcing." Thesis, Brunel University, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.309501.
Noubiagain, Chomchie Fanny Larissa. "Contributions to second order reflected backward stochastic differentials equations." Thesis, Le Mans, 2017. http://www.theses.fr/2017LEMA1016/document.
This thesis deals with the second-order reflected backward stochastic differential equations (2RBSDEs) in general filtration. In the first part , we consider the reflection with a lower obstacle and then extended the result in the case of an upper obstacle . Our main contribution consists in demonstrating the existence and the uniqueness of the solution of these equations defined in the general filtration under weak assumptions. We replace the uniform regularity by the Borel regularity(through analytic measurability). The dynamic programming principle for the robust stochastic control problem is thus demonstrated under weak assumptions, that is to say without regularity on the generator, the terminal condition and the obstacle. In the standard Backward Stochastic Differential Equations (BSDEs) framework, there is a symmetry between lower and upper obstacles reflection problem. On the contrary, in the context of second order BSDEs, this symmetry is no longer satisfy because of the nonlinearity of the expectation under which our robust stochastic non-dominated stochastic control problem is defined. In the second part , we get a numerical approximation scheme of a class of second-order reflected BSDEs. In particular we show the convergence of our scheme and we test numerically the results
Karlgaard, Christopher David. "Second-Order Relative Motion Equations." Thesis, Virginia Tech, 2001. http://hdl.handle.net/10919/34025.
Master of Science
Rodríguez, Cuesta Mª José. "Limit of detection for second-order calibration methods." Doctoral thesis, Universitat Rovira i Virgili, 2006. http://hdl.handle.net/10803/9013.
The lowest quantity of a substance that can be distinguished from the absence of that substance (a blank value) is called the detection limit or limit of detection (LOD). Traditionally, in the context of simple measurements where the instrumental signal only depends on the amount of analyte, a multiple of the blank value is taken to calculate the LOD (traditionally, the blank value plus three times the standard deviation of the measurement). However, the increasing complexity of the data that analytical instruments can provide for incoming samples leads to situations in which the LOD cannot be calculated as reliably as before.
Measurements, instruments and mathematical models can be classified according to the type of data they use. Tensorial theory provides a unified language that is useful for describing the chemical measurements, analytical instruments and calibration methods. Instruments that generate two-dimensional arrays of data are second-order instruments. A typical example is a spectrofluorometer, which provides a set of emission spectra obtained at different excitation wavelengths.
The calibration methods used with each type of data have different features and complexity. In this thesis, the most commonly used calibration methods are reviewed, from zero-order (or univariate) to second-order (or multi-linears) calibration models. Second-order calibration models are treated in details since they have been applied in the thesis.
Concretely, the following methods are described:
- PARAFAC (Parallel Factor Analysis)
- ITTFA (Iterative Target Transformation Analysis)
- MCR-ALS (Multivariate Curve Resolution-Alternating Least Squares)
- N-PLS (Multi-linear Partial Least Squares)
Analytical methods should be validated. The validation process typically starts by defining the scope of the analytical procedure, which includes the matrix, target analyte(s), analytical technique and intended purpose. The next step is to identify the performance characteristics that must be validated, which may depend on the purpose of the procedure, and the experiments for determining them. Finally, validation results should be documented, reviewed and maintained (if not, the procedure should be revalidated) as long as the procedure is applied in routine work.
The figures of merit of a chemical analytical process are 'those quantifiable terms which may indicate the extent of quality of the process. They include those terms that are closely related to the method and to the analyte (sensitivity, selectivity, limit of detection, limit of quantification, ...) and those which are concerned with the final results (traceability, uncertainty and representativity) (Inczédy et al., 1998). The aim of this thesis is to develop theoretical and practical strategies for calculating the limit of detection for complex analytical situations. Specifically, I focus on second-order calibration methods, i.e. when a matrix of data is available for each sample.
The methods most often used for making detection decisions are based on statistical hypothesis testing and involve a choice between two hypotheses about the sample. The first hypothesis is the "null hypothesis": the sample is analyte-free. The second hypothesis is the "alternative hypothesis": the sample is not analyte-free. In the hypothesis test there are two possible types of decision errors. An error of the first type occurs when the signal for an analyte-free sample exceeds the critical value, leading one to conclude incorrectly that the sample contains a positive amount of the analyte. This type of error is sometimes called a "false positive". An error of the second type occurs if one concludes that a sample does not contain the analyte when it actually does and it is known as a "false negative". In zero-order calibration, this hypothesis test is applied to the confidence intervals of the calibration model to estimate the LOD as proposed by Hubaux and Vos (A. Hubaux, G. Vos, Anal. Chem. 42: 849-855, 1970).
One strategy for estimating multivariate limits of detection is to transform the multivariate model into a univariate one. This strategy has been applied in this thesis in three practical applications:
1. LOD for PARAFAC (Parallel Factor Analysis).
2. LOD for ITTFA (Iterative Target Transformation Factor Analysis).
3. LOD for MCR-ALS (Multivariate Curve Resolution - Alternating Least Squares)
In addition, the thesis includes a theoretical contribution with the proposal of a sample-dependent LOD in the context of multivariate (PLS) and multi-linear (N-PLS) Partial Least Squares.
La Química Analítica es pot dividir en dos tipus d'anàlisis, l'anàlisi quantitativa i l'anàlisi qualitativa. La gran part de la química analítica moderna és quantitativa i fins i tot els govern fan ús d'aquesta ciència per establir regulacions que controlen, per exemple, nivells d'exposició a substàncies tòxiques que poden afectar la salut pública. El concepte de mínima quantitat d'un analit o component que es pot detectar apareix en moltes d'aquestes regulacions, en general com una part de la validació dels mètodes per tal de garantir la qualitat i la validesa dels resultats.
La mínima quantitat d'una substància que pot ser diferenciada de l'absència d'aquesta substància (el que es coneix com un blanc) s'anomena límit de detecció (limit of detection, LOD). En procediments on es treballa amb mesures analítiques que són degudes només a la quantitat d'analit present a la mostra (situació d'ordre zero) el LOD es pot calcular com un múltiple de la mesura del blanc (tradicionalment, 3 vegades la desviació d'aquesta mesura). Tanmateix, l'evolució dels instruments analítics i la complexitat creixent de les dades que generen, porta a situacions en les que el LOD no es pot calcular fiablement d'una forma tan senzilla. Les mesures, els instruments i els models de calibratge es poden classificar en funció del tipus de dades que utilitzen. La Teoria Tensorial s'ha utilitzat en aquesta tesi per fer aquesta classificació amb un llenguatge útil i unificat. Els instruments que generen dades en dues dimensions s'anomenen instruments de segon ordre i un exemple típic és l'espectrofluorímetre d'excitació-emissió, que proporciona un conjunt d'espectres d'emissió obtinguts a diferents longituds d'ona d'excitació.
Els mètodes de calibratge emprats amb cada tipus de dades tenen diferents característiques i complexitat. En aquesta tesi, es fa una revisió dels models de calibratge més habituals d'ordre zero (univariants), de primer ordre (multivariants) i de segon ordre (multilinears). Els mètodes de segon ordre estan tractats amb més detall donat que són els que s'han emprat en les aplicacions pràctiques portades a terme.
Concretament es descriuen:
- PARAFAC (Parallel Factor Analysis)
- ITTFA (Iterative Target Transformation Analysis)
- MCR-ALS (Multivariate Curve Resolution-Alternating Least Squares)
- N-PLS (Multi-linear Partial Least Squares)
Com s'ha avançat al principi, els mètodes analítics s'han de validar. El procés de validació inclou la definició dels límits d'aplicació del procediment analític (des del tipus de mostres o matrius fins l'analit o components d'interès, la tècnica analítica i l'objectiu del procediment). La següent etapa consisteix en identificar i estimar els paràmetres de qualitat (figures of merit, FOM) que s'han de validar per, finalment, documentar els resultats de la validació i mantenir-los mentre sigui aplicable el procediment descrit.
Algunes FOM dels processos químics de mesura són: sensibilitat, selectivitat, límit de detecció, exactitud, precisió, etc. L'objectiu principal d'aquesta tesi és desenvolupar estratègies teòriques i pràctiques per calcular el límit de detecció per problemes analítics complexos. Concretament, està centrat en els mètodes de calibratge que treballen amb dades de segon ordre.
Els mètodes més emprats per definir criteris de detecció estan basats en proves d'hipòtesis i impliquen una elecció entre dues hipòtesis sobre la mostra. La primera hipòtesi és la hipòtesi nul·la: a la mostra no hi ha analit. La segona hipòtesis és la hipòtesis alternativa: a la mostra hi ha analit. En aquest context, hi ha dos tipus d'errors en la decisió. L'error de primer tipus té lloc quan es determina que la mostra conté analit quan no en té i la probabilitat de cometre l'error de primer tipus s'anomena fals positiu. L'error de segon tipus té lloc quan es determina que la mostra no conté analit quan en realitat si en conté i la probabilitat d'aquest error s'anomena fals negatiu. En calibratges d'ordre zero, aquesta prova d'hipòtesi s'aplica als intervals de confiança de la recta de calibratge per calcular el LOD mitjançant les fórmules d'Hubaux i Vos (A. Hubaux, G. Vos, Anal. Chem. 42: 849-855, 1970)
Una estratègia per a calcular límits de detecció quan es treballa amb dades de segon ordre es transformar el model multivariant en un model univariant. Aquesta estratègia s'ha fet servir en la tesi en tres aplicacions diferents::
1. LOD per PARAFAC (Parallel Factor Analysis).
2. LOD per ITTFA (Iterative Target Transformation Factor Analysis).
3. LOD per MCR-ALS (Multivariate Curve Resolution - Alternating Least Squares)
A més, la tesi inclou una contribució teòrica amb la proposta d'un LOD que és específic per cada mostra, en el context del mètode multivariant PLS i del multilinear N-PLS.
Snyman, H. "Second order analyses methods for stirling engine design." Thesis, Stellenbosch : University of Stellenbosch, 2007. http://hdl.handle.net/10019.1/16102.
121 Leaves printed single pages, preliminary pages a-l and numbered pages 1-81.
ENGLISH ABSTRACT:In the midst of the current non-renewable energy crises specifically with regard to fossil fuel, various research institutions across the world have turned their focus to renewable and sustainable development. Using our available non.renewable resources as efficiently as possible has been a focal point the past decades and will certainly be as long as these resources exist Various means to utilize the world's abundant and freely available renewable energy has been studied and some even introduced and installed as sustainable energy sources, Electricity generation by means of wind powered turbines, photo-voltaic cells, and tidal and wave energy are but a few examples. Modern photo-voltaic cells are known to have a solar to electricity conversion efficiency of 12% (Van Heerden, 2003) while wind turbines have an approximate wind to electricity conversion efficiency of 50% (Twele et aI., 2002). This low solar to electricity conversion efficiency together with the fact that renewable energy research is a relatively modern development, lead to the investigation into methods capable of higher solar to electricity conversion efficiencies. One such method could be to use the relatively old technology of the Stirling cycle developed in the early 1800's (solar to electricity conversion efficiency in the range of 20.24 % according Van Heerden, 2003). The Stirling cycle provides a method for converting thermal energy to mechanical power which can be used to generate electricity, One of the main advantages of Stirling machines is that they are capable of using any form of heat source ranging from solar to biomass and waste heat. This document provides a discussion of some of the available methods for the analysis of Stirling machines. The six (6) different methods considered include: the method of Beale, West, mean-pressurepower- formula (MPPF), Schmidt, idea! adiabatic and the simple analysis methods. The first three (3) are known to be good back-of-the-envelope methods specifically for application as synthesis tools during initialisation of design procedures, while the latter three (3) are analysis tools finding application during Stirling engine design and analysis procedures. These analysis methods are based on the work done by Berchowitz and Urieli (1984) and form the centre of this document. Sections to follow provide a discussion of the mathematical model as well as the MATlAB implementation thereof. Experimental tests were conducted on the Heinrici engine to provide verification of the simulated resutls. Shortcomings of these analyses methods are also discussed in the sections to follow. Recommendations regarding improvements of the simulation program, possible fields of application for Stirling technology, as well as future fields of study are made in the final chapter of this document. A review of relevanl literature regarding modern applications of Stirling technology and listings of companies currently manufacturing and developing Stirling machines and findings of research done at various other institutions are provided.
AFRIKAANSE OPSOMMING:Die tempo van uitputling van die wereld se nie-hernubare energiebronne die afgelope jare het aanleiding gegee daartoe dal daar loenemend fokus toegespits word op die ontwikkeling van hernubare alternatiewe. Meer doeltreffende benutting van die wereld se nie-hernubare energie is reeds 'n fokus punt, vir navorsers reg oor die wereld, vir die afgelope dekades. Die aarde se oorvloedryke hernubare energie bronne word reeds met verskeie metodes ontgin. Die omskakeling van wind-, son- en gety energie na elektrisieteids is net 'n paar voorbeelde. Die effektiwiteid van sonkrag na elektrisietyds omskakeling van moderne fotovo!la'iese selle is in die orde van 12% (Van Heerden, 2003) terwyl die doeltreffendeid van wind energie na elektrisiteit omskakelling in die orde van 50% (Twele et at, 2002) is. Hierdie relatief lae omskelings doeltreffendeid van sonkrag na elektrisietyd, tesame met die feit dat die hernubare industrie nag relatief jonk is, lei lot die soeke na ander meer doellreffende moontlikhede Die Stirling siklus is nie 'n mod erne beginsel nie, maar die toepassing daarvan veral in die hernubare energie industrie is wei 'n relatiewe nuwe beg rip, veral in teme van die omskakeling van sonkrag na elektriese energie (gemiddelde sonkrag na lektriese energie omskakelings doellreffendeid in die orde van 20-24% is gevind deur Van Heerden, 2003). Die omskakeling van lermiese energie na meganiese energie is sekerlik die hoof uitkomsle van die Stirling siklus, alhoewel dit ook toepassing vind in die verkoefingsindustrie. Die feit dat die Stirling siklus van enige vorm van termiese energie (bv. son. biomassa, asook hilte geproduseer as byproduk tydens sekere prosesse) gebruik kan maak. is een van die redes wat die tegnologie 56 aanloklik maak, spesifiek !.o,v. die hernubare energie sektor. Ses (6) metodes vir die analise van die Stirling siklus word in hierdie dokument bespreek. Dit slui! die volgnde in: Beale-, West-, die gemiddelde-druk-krag-metode (GDKM), Schmidt-, adiabatiese- en die eenvoudige analise melodes. Die eerste drie (3) metodes is handige berekenings metodes Iydens die aanvangs en sinlesefase van Stirling enjin ontwerp, lerwyl die laaste drie (3) meer loegespils is op die volledige ontwerps- en analisefases gedurende die Stirling eniin ontwerps proses. Die drie (3) analise melodes is gebaseer op die werk wat deur Berchowitz en Urieli (1984) gedoen is en maak die kern van die dokument uit. Die wiskundige model, implimentering daarvan in MATlAB, sowel as die eksperimentele verifieering van die resultate word bespreek. Tekortkominge van die analise metodes word ook aangespreek in elke hoofsluk. Moontlikke verbeterings len opsigte van die verskeie aannames word in die finale hoofsluk van die dokumenl aangespreek. Verskeie voorgestelde riglings vir toekomslige navorsings projekle word ook in die finale hoofstuk van die dokument genoem. 'n Kort oorsig van die relevanle lileraluur in verband mel huidige loepassings van die Stirling legnologie, asook die name van maatskappye wal tans hierdie tegnologiee ontwikkel en vervaardig, word genoem.
Zhou, Chao. "Model Uncertainty in Finance and Second Order Backward Stochastic Differential Equations." Palaiseau, Ecole polytechnique, 2012. https://pastel.hal.science/docs/00/77/14/37/PDF/Thesis_ZHOU_Chao_Pastel.pdfcc.
The main objective of this PhD thesis is to study some financial mathematics problems in an incomplete market with model uncertainty. In recent years, the theory of second order backward stochastic differential equations (2BSDEs for short) has been developed by Soner, Touzi and Zhang on this topic. In this thesis, we adopt their point of view. This thesis contains of four key parts related to 2BSDEs. In the first part, we generalize the 2BSDEs theory initially introduced in the case of Lipschitz continuous generators to quadratic growth generators. This new class of 2BSDEs will then allow us to consider the robust utility maximization problem in non-dominated models. In the second part, we study this problem for exponential utility, power utility and logarithmic utility. In each case, we give a characterization of the value function and an optimal investment strategy via the solution to a 2BSDE. In the third part, we provide an existence and uniqueness result for second order reflected BSDEs with lower obstacles and Lipschitz generators, and then we apply this result to study the problem of American contingent claims pricing with uncertain volatility. In the fourth part, we define a notion of 2BSDEs with jumps, for which we prove the existence and uniqueness of solutions in appropriate spaces. We can interpret these equations as standard BSDEs with jumps, under both volatility and jump measure uncertainty. As an application of these results, we shall study a robust exponential utility maximization problem under model uncertainty, where the uncertainty affects both the volatility process and the jump measure
Books on the topic "Stochastic second order methods":
Kakihara, Yūichirō. Multidimensional second order stochastic processes. Singapore: World Scientific, 1997.
Lan, Guanghui. First-order and Stochastic Optimization Methods for Machine Learning. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-39568-1.
Shepherd, Adrian J. Second-Order Methods for Neural Networks. London: Springer London, 1997. http://dx.doi.org/10.1007/978-1-4471-0953-2.
Strassert, Günter. The balancing principle, strict superiority relations, and a transitive overall final order of options. Karlsruhe: Institut für Regionalwissenschaft der Universität Karlsruhe, 2000.
Otmani, Zoulikha Zaidi ep. Numerical methods for second order parabolic partial differential equations. Uxbridge: Brunel University, 1986.
Aamir, Shabbir, and United States. National Aeronautics and Space Administration., eds. Methods of ensuring realizability for non-realizable second order closures. [Washington, DC]: National Aeronautics and Space Administration, 1994.
Shepherd, Adrian J. Second-order methods for neural networks: Fast and reliable training methods for multi-layer perceptrons. London: Springer, 1997.
Krispin, J. Second-order Godunov methods and self-similar steady supersonic three-dimensional flowfields. Washington, D. C: American Institute of Aeronautics and Astronautics, 1991.
Courcelle, B. Graph structure and monadic second-order logic: A language-theoretic approach. Cambridge: Cambridge University Press, 2012.
Heinrich, Bernd. Finite difference methods on irregular networks: A generalized approach to second order elliptic problems. Basel: Birkhäuser Verlag, 1987.
Book chapters on the topic "Stochastic second order methods":
Heindl, Armin, Gábor Horváth, and Karsten Gross. "Explicit Inverse Characterizations of Acyclic MAPs of Second Order." In Formal Methods and Stochastic Models for Performance Evaluation, 108–22. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11777830_8.
Cannarsa, P., and G. Da Prato. "Second order Hamilton-Jacobi equations in infinite dimensions and stochastic optimal control problems." In Probabilistic and Stochastic Methods in Analysis, with Applications, 617–29. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2791-2_30.
Fábián, Csaba I., Gautam Mitra, Diana Roman, Victor Zverovich, Tibor Vajnai, Edit Csizmás, and Olga Papp. "Portfolio Choice Models Based on Second-Order Stochastic Dominance Measures: An Overview and a Computational Study." In Stochastic Optimization Methods in Finance and Energy, 441–69. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-9586-5_18.
Vatanen, Tommi, Tapani Raiko, Harri Valpola, and Yann LeCun. "Pushing Stochastic Gradient towards Second-Order Methods – Backpropagation Learning with Transformations in Nonlinearities." In Neural Information Processing, 442–49. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-42054-2_55.
Gao, Hongchang, and Heng Huang. "Faster Stochastic Second Order Method for Large-Scale Machine Learning Models." In Proceedings of the 2021 SIAM International Conference on Data Mining (SDM), 405–13. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2021. http://dx.doi.org/10.1137/1.9781611976700.46.
Ben Arous, Gérard, and Peter Laurence. "Second Order Expansion for Implied Volatility in Two Factor Local Stochastic Volatility Models and Applications to the Dynamic $$\lambda $$ -Sabr Model." In Large Deviations and Asymptotic Methods in Finance, 89–136. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-11605-1_4.
Zhang, Jianfeng. "Second Order BSDEs." In Backward Stochastic Differential Equations, 335–64. New York, NY: Springer New York, 2017. http://dx.doi.org/10.1007/978-1-4939-7256-2_12.
Rozovskii, B. L. "Ito’s Second Order Parabolic Equations." In Stochastic Evolution Systems, 125–74. Dordrecht: Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-011-3830-7_4.
Rozovsky, Boris L., and Sergey V. Lototsky. "Itô’s Second-Order Parabolic Equations." In Stochastic Evolution Systems, 123–70. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94893-5_4.
Nesterov, Yurii. "Second-Order Methods." In Lectures on Convex Optimization, 241–322. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-91578-4_4.
Conference papers on the topic "Stochastic second order methods":
Agafonov, Artem, Pavel Dvurechensky, Gesualdo Scutari, Alexander Gasnikov, Dmitry Kamzolov, Aleksandr Lukashevich, and Amir Daneshmand. "An Accelerated Second-Order Method for Distributed Stochastic Optimization." In 2021 60th IEEE Conference on Decision and Control (CDC). IEEE, 2021. http://dx.doi.org/10.1109/cdc45484.2021.9683400.
Gao, Hongchang, and Heng Huang. "Stochastic Second-Order Method for Large-Scale Nonconvex Sparse Learning Models." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/294.
Canhanga, Betuel, Ying Ni, Milica Rančić, Anatoliy Malyarenko, and Sergei Silvestrov. "Numerical methods on European option second order asymptotic expansions for multiscale stochastic volatility." In ICNPAA 2016 WORLD CONGRESS: 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences. Author(s), 2017. http://dx.doi.org/10.1063/1.4972627.
Naess, A., and H. C. Karlsen. "Nonlinear, Second-Order Response Statistics of Compliant Offshore Structures." In ASME 2003 22nd International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2003. http://dx.doi.org/10.1115/omae2003-37127.
Mane, Vibha, Monica F. Bugallo, and Petar M. Djuric. "Stochastic modeling of second order reactions using a moment propagation method." In 2009 IEEE International Workshop on Genomic Signal Processing and Statistics (GENSIPS). IEEE, 2009. http://dx.doi.org/10.1109/gensips.2009.5174358.
Tang, Rui. "A New Second-order Bistable Adaptive Stochastic Resonance Noise Reduction Method." In 8th International Conference on Social Network, Communication and Education (SNCE 2018). Paris, France: Atlantis Press, 2018. http://dx.doi.org/10.2991/snce-18.2018.25.
Jensen, Jo̸rgen Juncher. "Extreme Response Predictions for Jack-Up Units in Second Order Stochastic Waves by FORM." In ASME 2007 26th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2007. http://dx.doi.org/10.1115/omae2007-29022.
Naess, A., H. C. Karlsen, and P. S. Teigen. "Accurate Numerical Methods for Calculating the Response Statistics of Compliant Offshore Structures." In ASME 2005 24th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2005. http://dx.doi.org/10.1115/omae2005-67236.
Snyder, Donald L., and Timothy J. Schulz. "Some new methods for restoring images of faint objects." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1991. http://dx.doi.org/10.1364/oam.1991.ft1.
Li, Zhijian, Chao Zhang, Hui Qian, Xin Du, and Lingwei Peng. "SHPOS: A Theoretical Guaranteed Accelerated Particle Optimization Sampling Method." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/372.
Reports on the topic "Stochastic second order methods":
Petersson, N., and B. Sjogreen. Serpentine: Finite Difference Methods for Wave Propagation in Second Order Formulation. Office of Scientific and Technical Information (OSTI), March 2012. http://dx.doi.org/10.2172/1046802.
Mitchell, Jason W. Implementing Families of Implicit Chebyshev Methods with Exact Coefficients for the Numerical Integration of First- and Second-Order Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, May 2002. http://dx.doi.org/10.21236/ada404958.
Rutan, S. C. Enhancement of fluorescence detection in chromatographic methods by computer analysis of second order data. Progress report, August 1, 1990--October 1, 1993. Office of Scientific and Technical Information (OSTI), December 1993. http://dx.doi.org/10.2172/10163516.
Nobile, F., Q. Ayoul-Guilmard, S. Ganesh, M. Nuñez, A. Kodakkal, C. Soriano, and R. Rossi. D6.5 Report on stochastic optimisation for wind engineering. Scipedia, 2022. http://dx.doi.org/10.23967/exaqute.2022.3.04.
Соловйов, Володимир Миколайович, and D. N. Chabanenko. Financial crisis phenomena: analysis, simulation and prediction. Econophysic’s approach. Гумбольдт-Клуб Україна, November 2009. http://dx.doi.org/10.31812/0564/1138.
Escobar Hernández, José Carlos. Working paper PUEAA No. 15. Teaching Spanish to Japanese students: The students’ profile, their needs and their learning style. Universidad Nacional Autónoma de México, Programa Universitario de Estudios sobre Asia y África, 2022. http://dx.doi.org/10.22201/pueaa.013r.2022.
Gupte, Jaideep, Louise Clark, Debjani Ghosh, Sarath Babu, Priyanka Mehra, Asif Raza, Vaibhav Sharma, et al. Embedding Community Voice into Smart City Spatial Planning. Institute of Development Studies, February 2022. http://dx.doi.org/10.19088/ids.2022.005.
Oliver, Sandy, Dayana Minchenko, Mukdarut Bangpan, Kelly Dickson, Claire Stansfield, and Janice Tripney. Evidence claims for informing decisions relating to socio-economic development. Centre for Excellence and Development Impact and Learning (CEDIL), April 2023. http://dx.doi.org/10.51744/llp2.
Bauza, Rodrigo, and Daniel Olsen. PR-179-20200-R01 Improved Catalyst Regeneration Process to Increase Poison Removal. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), June 2021. http://dx.doi.org/10.55274/r0012106.
Fieseler, Kelsey, and Timothy Jacobs. PR-457-14201-R04 Variable NG Composition Effects on LB 2SC Integral Engines. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), September 2018. http://dx.doi.org/10.55274/r0011525.