Numerical Methods For Stochastic Computations

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Numerical Methods for Stochastic Computations

Dongbin Xiu
Numerical Methods for Stochastic Computations Book PDF

Author : Dongbin Xiu
Publisher : Princeton University Press
Page : 142 pages
File Size : 55,5 Mb
Release : 2010-07-01
Category : Mathematics
ISBN : 9781400835348

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Numerical Methods for Stochastic Computations by Dongbin Xiu Pdf

The@ first graduate-level textbook to focus on fundamental aspects of numerical methods for stochastic computations, this book describes the class of numerical methods based on generalized polynomial chaos (gPC). These fast, efficient, and accurate methods are an extension of the classical spectral methods of high-dimensional random spaces. Designed to simulate complex systems subject to random inputs, these methods are widely used in many areas of computer science and engineering. The book introduces polynomial approximation theory and probability theory; describes the basic theory of gPC methods through numerical examples and rigorous development; details the procedure for converting stochastic equations into deterministic ones; using both the Galerkin and collocation approaches; and discusses the distinct differences and challenges arising from high-dimensional problems. The last section is devoted to the application of gPC methods to critical areas such as inverse problems and data assimilation. Ideal for use by graduate students and researchers both in the classroom and for self-study, Numerical Methods for Stochastic Computations provides the required tools for in-depth research related to stochastic computations. The first graduate-level textbook to focus on the fundamentals of numerical methods for stochastic computations Ideal introduction for graduate courses or self-study Fast, efficient, and accurate numerical methods Polynomial approximation theory and probability theory included Basic gPC methods illustrated through examples

Numerical Methods for Stochastic Control Problems in Continuous Time

Harold Kushner,Paul G. Dupuis
Numerical Methods for Stochastic Control Problems in Continuous Time Book PDF

Author : Harold Kushner,Paul G. Dupuis
Publisher : Springer Science & Business Media
Page : 480 pages
File Size : 46,6 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9781461300076

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Numerical Methods for Stochastic Control Problems in Continuous Time by Harold Kushner,Paul G. Dupuis Pdf

Stochastic control is a very active area of research. This monograph, written by two leading authorities in the field, has been updated to reflect the latest developments. It covers effective numerical methods for stochastic control problems in continuous time on two levels, that of practice and that of mathematical development. It is broadly accessible for graduate students and researchers.

Computational Methods in Stochastic Dynamics

Manolis Papadrakakis,George Stefanou,Vissarion Papadopoulos
Computational Methods in Stochastic Dynamics Book PDF

Author : Manolis Papadrakakis,George Stefanou,Vissarion Papadopoulos
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 40,8 Mb
Release : 2011-02-01
Category : Technology & Engineering
ISBN : 9789048199877

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Computational Methods in Stochastic Dynamics by Manolis Papadrakakis,George Stefanou,Vissarion Papadopoulos Pdf

At the dawn of the 21st century, computational stochastic dynamics is an emerging research frontier. This book focuses on advanced computational methods and software tools which can highly assist in tackling complex problems in stochastic dynamic/seismic analysis and design of structures. The book is primarily intended for researchers and post-graduate students in the fields of computational mechanics and stochastic structural dynamics. Nevertheless, practice engineers as well could benefit from it as most code provisions tend to incorporate probabilistic concepts in the analysis and design of structures. The book addresses mathematical and numerical issues in stochastic structural dynamics and connects them to real-world applications. It consists of 16 chapters dealing with recent advances in a wide range of related topics (dynamic response variability and reliability of stochastic systems, risk assessment, stochastic simulation of earthquake ground motions, efficient solvers for the analysis of stochastic systems, dynamic stability, stochastic modelling of heterogeneous materials). Numerical examples demonstrating the significance of the proposed methods are presented in each chapter.

Stochastic Numerics for the Boltzmann Equation

Sergej Rjasanow,Wolfgang Wagner
Stochastic Numerics for the Boltzmann Equation Book PDF

Author : Sergej Rjasanow,Wolfgang Wagner
Publisher : Springer Science & Business Media
Page : 266 pages
File Size : 55,5 Mb
Release : 2005-11-04
Category : Mathematics
ISBN : 9783540276890

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Stochastic Numerics for the Boltzmann Equation by Sergej Rjasanow,Wolfgang Wagner Pdf

Stochastic numerical methods play an important role in large scale computations in the applied sciences. The first goal of this book is to give a mathematical description of classical direct simulation Monte Carlo (DSMC) procedures for rarefied gases, using the theory of Markov processes as a unifying framework. The second goal is a systematic treatment of an extension of DSMC, called stochastic weighted particle method. This method includes several new features, which are introduced for the purpose of variance reduction (rare event simulation). Rigorous convergence results as well as detailed numerical studies are presented.

Numerical methods and stochastics

T. J. Lyons
Numerical methods and stochastics Book PDF

Author : T. J. Lyons
Publisher : Unknown
Page : 128 pages
File Size : 46,9 Mb
Release : 2002
Category : Numerical analysis
ISBN : 1470430681

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Numerical methods and stochastics by T. J. Lyons Pdf

This volume represents the proceedings of the Workshop on Numerical Methods and Stochastics held at The Fields Institute in April 1999. The goal of the workshop was to identify emerging ideas in probability theory that influence future work in both probability and numerical computation. The book focuses on new results and gives novel approaches to computational problems based on the latest techniques from the theory of probability and stochastic processes. Three papers discuss particle system approximations to solutions of the stochastic filtering problem. Two papers treat particle system equa.

An Introduction to Computational Stochastic PDEs

Gabriel J. Lord,Catherine E. Powell,Tony Shardlow
An Introduction to Computational Stochastic PDEs Book PDF

Author : Gabriel J. Lord,Catherine E. Powell,Tony Shardlow
Publisher : Cambridge University Press
Page : 516 pages
File Size : 44,5 Mb
Release : 2014-08-11
Category : Mathematics
ISBN : 9781139915779

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An Introduction to Computational Stochastic PDEs by Gabriel J. Lord,Catherine E. Powell,Tony Shardlow Pdf

This book gives a comprehensive introduction to numerical methods and analysis of stochastic processes, random fields and stochastic differential equations, and offers graduate students and researchers powerful tools for understanding uncertainty quantification for risk analysis. Coverage includes traditional stochastic ODEs with white noise forcing, strong and weak approximation, and the multi-level Monte Carlo method. Later chapters apply the theory of random fields to the numerical solution of elliptic PDEs with correlated random data, discuss the Monte Carlo method, and introduce stochastic Galerkin finite-element methods. Finally, stochastic parabolic PDEs are developed. Assuming little previous exposure to probability and statistics, theory is developed in tandem with state-of-the-art computational methods through worked examples, exercises, theorems and proofs. The set of MATLAB® codes included (and downloadable) allows readers to perform computations themselves and solve the test problems discussed. Practical examples are drawn from finance, mathematical biology, neuroscience, fluid flow modelling and materials science.

Stochastic Simulation and Monte Carlo Methods

Carl Graham,Denis Talay
Stochastic Simulation and Monte Carlo Methods Book PDF

Author : Carl Graham,Denis Talay
Publisher : Springer Science & Business Media
Page : 264 pages
File Size : 51,5 Mb
Release : 2013-07-16
Category : Mathematics
ISBN : 9783642393631

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Stochastic Simulation and Monte Carlo Methods by Carl Graham,Denis Talay Pdf

In various scientific and industrial fields, stochastic simulations are taking on a new importance. This is due to the increasing power of computers and practitioners’ aim to simulate more and more complex systems, and thus use random parameters as well as random noises to model the parametric uncertainties and the lack of knowledge on the physics of these systems. The error analysis of these computations is a highly complex mathematical undertaking. Approaching these issues, the authors present stochastic numerical methods and prove accurate convergence rate estimates in terms of their numerical parameters (number of simulations, time discretization steps). As a result, the book is a self-contained and rigorous study of the numerical methods within a theoretical framework. After briefly reviewing the basics, the authors first introduce fundamental notions in stochastic calculus and continuous-time martingale theory, then develop the analysis of pure-jump Markov processes, Poisson processes, and stochastic differential equations. In particular, they review the essential properties of Itô integrals and prove fundamental results on the probabilistic analysis of parabolic partial differential equations. These results in turn provide the basis for developing stochastic numerical methods, both from an algorithmic and theoretical point of view. The book combines advanced mathematical tools, theoretical analysis of stochastic numerical methods, and practical issues at a high level, so as to provide optimal results on the accuracy of Monte Carlo simulations of stochastic processes. It is intended for master and Ph.D. students in the field of stochastic processes and their numerical applications, as well as for physicists, biologists, economists and other professionals working with stochastic simulations, who will benefit from the ability to reliably estimate and control the accuracy of their simulations.

Numerical Methods for Controlled Stochastic Delay Systems

Harold Kushner
Numerical Methods for Controlled Stochastic Delay Systems Book PDF

Author : Harold Kushner
Publisher : Springer Science & Business Media
Page : 295 pages
File Size : 49,9 Mb
Release : 2008-12-19
Category : Science
ISBN : 9780817646219

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Numerical Methods for Controlled Stochastic Delay Systems by Harold Kushner Pdf

The Markov chain approximation methods are widely used for the numerical solution of nonlinear stochastic control problems in continuous time. This book extends the methods to stochastic systems with delays. The book is the first on the subject and will be of great interest to all those who work with stochastic delay equations and whose main interest is either in the use of the algorithms or in the mathematics. An excellent resource for graduate students, researchers, and practitioners, the work may be used as a graduate-level textbook for a special topics course or seminar on numerical methods in stochastic control.

Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology

David Holcman
Stochastic Processes Multiscale Modeling and Numerical Methods for Computational Cellular Biology Book PDF

Author : David Holcman
Publisher : Springer
Page : 377 pages
File Size : 45,8 Mb
Release : 2017-10-04
Category : Mathematics
ISBN : 9783319626277

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Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology by David Holcman Pdf

This book focuses on the modeling and mathematical analysis of stochastic dynamical systems along with their simulations. The collected chapters will review fundamental and current topics and approaches to dynamical systems in cellular biology. This text aims to develop improved mathematical and computational methods with which to study biological processes. At the scale of a single cell, stochasticity becomes important due to low copy numbers of biological molecules, such as mRNA and proteins that take part in biochemical reactions driving cellular processes. When trying to describe such biological processes, the traditional deterministic models are often inadequate, precisely because of these low copy numbers. This book presents stochastic models, which are necessary to account for small particle numbers and extrinsic noise sources. The complexity of these models depend upon whether the biochemical reactions are diffusion-limited or reaction-limited. In the former case, one needs to adopt the framework of stochastic reaction-diffusion models, while in the latter, one can describe the processes by adopting the framework of Markov jump processes and stochastic differential equations. Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology will appeal to graduate students and researchers in the fields of applied mathematics, biophysics, and cellular biology.

Stochastic Numerics for Mathematical Physics

Grigori Noah Milstein,Michael V. Tretyakov
Stochastic Numerics for Mathematical Physics Book PDF

Author : Grigori Noah Milstein,Michael V. Tretyakov
Publisher : Springer
Page : 596 pages
File Size : 54,7 Mb
Release : 2004-05-26
Category : Science
ISBN : 3540211101

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Stochastic Numerics for Mathematical Physics by Grigori Noah Milstein,Michael V. Tretyakov Pdf

Stochastic differential equations have many applications in the natural sciences. Besides, the employment of probabilistic representations together with the Monte Carlo technique allows us to reduce solution of multi-dimensional problems for partial differential equations to integration of stochastic equations. This approach leads to powerful computational mathematics that is presented in the treatise. The authors propose many new special schemes, some published here for the first time. In the second part of the book they construct numerical methods for solving complicated problems for partial differential equations occurring in practical applications, both linear and nonlinear. All the methods are presented with proofs and hence founded on rigorous reasoning, thus giving the book textbook potential. An overwhelming majority of the methods are accompanied by the corresponding numerical algorithms which are ready for implementation in practice. The book addresses researchers and graduate students in numerical analysis, physics, chemistry, and engineering as well as mathematical biology and financial mathematics.

An Introduction to Computational Stochastic PDEs

Gabriel J. Lord,Catherine E. Powell,Tony Shardlow
An Introduction to Computational Stochastic PDEs Book PDF

Author : Gabriel J. Lord,Catherine E. Powell,Tony Shardlow
Publisher : Cambridge University Press
Page : 0 pages
File Size : 55,5 Mb
Release : 2014-07-16
Category : Mathematics
ISBN : 1139898132

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An Introduction to Computational Stochastic PDEs by Gabriel J. Lord,Catherine E. Powell,Tony Shardlow Pdf

This book gives a comprehensive introduction to numerical methods and analysis of stochastic processes, random fields and stochastic differential equations, and offers graduate students and researchers powerful tools for understanding uncertainty quantification for risk analysis. Coverage includes traditional stochastic ODEs with white noise forcing, strong and weak approximation, and the multi-level Monte Carlo method. Later chapters apply the theory of random fields to the numerical solution of elliptic PDEs with correlated random data, discuss the Monte Carlo method, and introduce stochastic Galerkin finite-element methods. Finally, stochastic parabolic PDEs are developed. Assuming little previous exposure to probability and statistics, theory is developed in tandem with state-of the art computational methods through worked examples, exercises, theorems and proofs. The set of MATLAB codes included (and downloadable) allows readers to perform computations themselves and solve the test problems discussed. Practical examples are drawn from finance, mathematical biology, neuroscience, fluid flow modeling and materials science.

Spectral Methods for Uncertainty Quantification

Olivier Le Maitre,Omar M Knio
Spectral Methods for Uncertainty Quantification Book PDF

Author : Olivier Le Maitre,Omar M Knio
Publisher : Springer Science & Business Media
Page : 542 pages
File Size : 47,6 Mb
Release : 2010-03-11
Category : Science
ISBN : 9789048135202

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Spectral Methods for Uncertainty Quantification by Olivier Le Maitre,Omar M Knio Pdf

This book deals with the application of spectral methods to problems of uncertainty propagation and quanti?cation in model-based computations. It speci?cally focuses on computational and algorithmic features of these methods which are most useful in dealing with models based on partial differential equations, with special att- tion to models arising in simulations of ?uid ?ows. Implementations are illustrated through applications to elementary problems, as well as more elaborate examples selected from the authors’ interests in incompressible vortex-dominated ?ows and compressible ?ows at low Mach numbers. Spectral stochastic methods are probabilistic in nature, and are consequently rooted in the rich mathematical foundation associated with probability and measure spaces. Despite the authors’ fascination with this foundation, the discussion only - ludes to those theoretical aspects needed to set the stage for subsequent applications. The book is authored by practitioners, and is primarily intended for researchers or graduate students in computational mathematics, physics, or ?uid dynamics. The book assumes familiarity with elementary methods for the numerical solution of time-dependent, partial differential equations; prior experience with spectral me- ods is naturally helpful though not essential. Full appreciation of elaborate examples in computational ?uid dynamics (CFD) would require familiarity with key, and in some cases delicate, features of the associated numerical methods. Besides these shortcomings, our aim is to treat algorithmic and computational aspects of spectral stochastic methods with details suf?cient to address and reconstruct all but those highly elaborate examples.

Numerical Methods and Stochastics

T. J. Lyons,Thomas Stephenson Salisbury
Numerical Methods and Stochastics Book PDF

Author : T. J. Lyons,Thomas Stephenson Salisbury
Publisher : American Mathematical Soc.
Page : 132 pages
File Size : 43,7 Mb
Release : 2024-07-03
Category : Mathematics
ISBN : 0821871404

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Numerical Methods and Stochastics by T. J. Lyons,Thomas Stephenson Salisbury Pdf

This volume represents the proceedings of the Workshop on Numerical Methods and Stochastics held at The Fields Institute in April 1999. The goal of the workshop was to identify emerging ideas in probability theory that influence future work in both probability and numerical computation. The book focuses on new results and gives novel approaches to computational problems based on the latest techniques from the theory of probability and stochastic processes. Three papers discussparticle system approximations to solutions of the stochastic filtering problem. Two papers treat particle system equations. The paper on ''rough paths'' describes how to generate good approximations to stochastic integrals. An expository paper discusses a long-standing conjecture: the stochastic fastdynamo effect. A final paper gives an analysis of the error in binomial and trinomial approximations to solutions of the Black-Scholes stochastic differential equations. The book is intended for graduate students and research mathematicians interested in probability theory.

Parallel and Distributed Computation: Numerical Methods

Dimitri Bertsekas,John Tsitsiklis
Parallel and Distributed Computation Numerical Methods Book PDF

Author : Dimitri Bertsekas,John Tsitsiklis
Publisher : Athena Scientific
Page : 832 pages
File Size : 54,9 Mb
Release : 2015-03-01
Category : Mathematics
ISBN : 9781886529151

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Parallel and Distributed Computation: Numerical Methods by Dimitri Bertsekas,John Tsitsiklis Pdf

This highly acclaimed work, first published by Prentice Hall in 1989, is a comprehensive and theoretically sound treatment of parallel and distributed numerical methods. It focuses on algorithms that are naturally suited for massive parallelization, and it explores the fundamental convergence, rate of convergence, communication, and synchronization issues associated with such algorithms. This is an extensive book, which aside from its focus on parallel and distributed algorithms, contains a wealth of material on a broad variety of computation and optimization topics. It is an excellent supplement to several of our other books, including Convex Optimization Algorithms (Athena Scientific, 2015), Nonlinear Programming (Athena Scientific, 1999), Dynamic Programming and Optimal Control (Athena Scientific, 2012), Neuro-Dynamic Programming (Athena Scientific, 1996), and Network Optimization (Athena Scientific, 1998). The on-line edition of the book contains a 95-page solutions manual.

Deterministic and Stochastic Modeling in Computational Electromagnetics

Dragan Poljak,Anna Susnjara
Deterministic and Stochastic Modeling in Computational Electromagnetics Book PDF

Author : Dragan Poljak,Anna Susnjara
Publisher : John Wiley & Sons
Page : 580 pages
File Size : 50,5 Mb
Release : 2023-12-07
Category : Science
ISBN : 9781119989240

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Deterministic and Stochastic Modeling in Computational Electromagnetics by Dragan Poljak,Anna Susnjara Pdf

Deterministic and Stochastic Modeling in Computational Electromagnetics Help protect your network with this important reference work on cyber security Deterministic computational models are those for which all inputs are precisely known, whereas stochastic modeling reflects uncertainty or randomness in one or more of the data inputs. Many problems in computational engineering therefore require both deterministic and stochastic modeling to be used in parallel, allowing for different degrees of confidence and incorporating datasets of different kinds. In particular, non-intrusive stochastic methods can be easily combined with widely used deterministic approaches, enabling this more robust form of data analysis to be applied to a range of computational challenges. Deterministic and Stochastic Modeling in Computational Electromagnetics provides a rare treatment of parallel deterministic–stochastic computational modeling and its beneficial applications. Unlike other works of its kind, which generally treat deterministic and stochastic modeling in isolation from one another, it aims to demonstrate the usefulness of a combined approach and present particular use-cases in which such an approach is clearly required. It offers a non-intrusive stochastic approach which can be incorporated with minimal effort into virtually all existing computational models. Readers will also find: A range of specific examples demonstrating the efficiency of deterministic–stochastic modeling Computational examples of successful applications including ground penetrating radars (GPR), radiation from 5G systems, transcranial magnetic and electric stimulation (TMS and TES), and more Introduction to fundamental principles in field theory to ground the discussion of computational modeling Deterministic and Stochastic Modeling in Computational Electromagnetics is a valuable reference for researchers, including graduate and undergraduate students, in computational electromagnetics, as well as to multidisciplinary researchers, engineers, physicists, and mathematicians.