Taylor Approximations for Stochastic Partial Differential Equations

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This book presents a systematic theory of Taylor expansions of evolutionary-type stochastic partial differential equations (SPDEs). The authors show how Taylor expansions can be used to derive higher order numerical methods for SPDEs, with a focus on pathwise and strong convergence.

In the case of multiplicative noise, the driving noise process is assumed to be a cylindrical Wiener process, while in the case of additive noise the SPDE is assumed to be driven by an arbitrary stochastic process with Hölder continuous sample paths. Recent developments on numerical methods for random and stochastic ordinary differential equations are also included since these are relevant for solving spatially discretised SPDEs as well as of interest in their own right.

The authors include the proof of an existence and uniqueness theorem under general assumptions on the coefficients as well as regularity estimates in an appendix.

Audience: Applied and pure mathematicians interested in using and further developing numerical methods for SPDEs will find this book helpful. It may also be used as a source of material for a graduate course.

Contents: Preface; List of Figures; Chapter 1: Introduction; Part I: Random and Stochastic Ordinary Partial Differential Equations; Chapter 2: RODEs; Chapter 3: SODEs; Chapter 4: SODEs with Nonstandard Assumptions; Part II: Stochastic Partial Differential Equations; Chapter 5: SPDEs; Chapter 6: Numerical Methods for SPDEs; Chapter 7: Taylor Approximations for SPDEs with Additive Noise; Chapter 8: Taylor Approximations for SPDEs with Multiplicative Noise; Appendix: Regularity Estimates for SPDEs; Bibliography; Index.

Editorial ReviewsBook DescriptionA comprehensive exposition of a systematic theory of Taylor expansions of evolutionary-type stochastic partial differential equations (SPDEs). Applied and pure mathematicians interested in using and further developing numerical methods for SPDEs will find this book helpful.

About the AuthorArnulf Jentzen is appointed as a Visiting Fellow in the Department of Applied and Computational Mathematics at Princeton University. His research focuses on analytical and numerical aspects of stochastic differential equations with non-globally Lipschitz continuous nonlinearities. Peter E. Kloeden is a Professor of Applied and Instrumental Mathematics at Goethe University Frankfurt am Main. He is a Fellow both of SIAM and of the Australian Mathematical Society. He was awarded the W.T. and Idalia Reid Prize in Mathematics by SIAM in 2006 for his fundamental contributions to the theoretical and computational analysis of differential equations.

Product Details

• Series: CBMS-NSF Regional Conference Series in Applied Mathematics (Book 83)
• Paperback: 234 pages
• Publisher: SIAM-Society for Industrial and Applied Mathematics (November 18, 2011)
• Language: English
• ISBN-10: 1611972000
• ISBN-13: 978-1611972009
  

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关键词：Differential Stochastic Different Equations equation Taylor

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