Stochastic numerics for mathematical physics / Grigori N. Milstein, Michael V. Tretyakov.
Milʹshteĭn, G. N. (Grigoriĭ Noĭkhovich), author.; Tretyakov, Michael V., author.
2021
QA274.23
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Title Stochastic numerics for mathematical physics / Grigori N. Milstein, Michael V. Tretyakov.
Author Milʹshteĭn, G. N. (Grigoriĭ Noĭkhovich), author.
Edition Second edition.
ISBN 9783030820404 (electronic bk.)
3030820408 (electronic bk.)
3030820394
9783030820398
DOI https://doi.org/10.1007/978-3-030-82040-4
Publication Details Cham, Switzerland : Springer, 2021.
Language English
Description 1 online resource
Item Number 10.1007/978-3-030-82040-4 doi
Call Number QA274.23
Dewey Decimal Classification 519.2/2
Summary This book is a substantially revised and expanded edition reflecting major developments in stochastic numerics since the first edition was published in 2004. The new topics, in particular, include mean-square and weak approximations in the case of nonglobally Lipschitz coefficients of Stochastic Differential Equations (SDEs) including the concept of rejecting trajectories; conditional probabilistic representations and their application to practical variance reduction using regression methods; multi-level Monte Carlo method; computing ergodic limits and additional classes of geometric integrators used in molecular dynamics; numerical methods for FBSDEs; approximation of parabolic SPDEs and nonlinear filtering problem based on the method of characteristics. SDEs have many applications in the natural sciences and in finance. Besides, the employment of probabilistic representations together with the Monte Carlo technique allows us to reduce the solution of multi-dimensional problems for partial differential equations to the integration of stochastic equations. This approach leads to powerful computational mathematics that is presented in the treatise. Many special schemes for SDEs are presented. In the second part of the book numerical methods for solving complicated problems for partial differential equations occurring in practical applications, both linear and nonlinear, are constructed. 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, applied probability, physics, chemistry, and engineering as well as mathematical biology and financial mathematics.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Digital File Characteristics text file
PDF
Source of Description Online resource; title from PDF title page (SpringerLink, viewed December 13, 2021).
Added Author Tretyakov, Michael V., author.
Series Scientific computation, 2198-2589
Available in Other Form Print version: 9783030820398
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Mean-square Approximation for Stochastic Di

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