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Taylor Approximations for Stochastic Partial Differential Equations

  • Paperback
A comprehensive exposition of a systematic theory of Taylor expansions of evolutionary-type stochastic partial differential equations.
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 Holder 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.
Arnulf 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.
Preface; List of figures; 1. Introduction; Part I. Random and Stochastic Ordinary Partial Differential Equations: 2. RODEs; 3. SODEs; 4. SODEs with nonstandard assumptions; Part II. Stochastic Partial Differential Equations: 5. SPDEs; 6. Numerical methods for SPDEs; 7. Taylor approximations for SPDEs with additive noise; 8. Taylor approximations for SPDEs with multiplicative noise; Appendix: regularity estimates for SPDEs; Bibliography; Index.
Author
Arnulf Jentzen, Peter E. Kloeden
Pages
235
Publisher
Society for Industrial & Applied Mathematics,U.S.
Series
CBMS-NSF Regional Conference Series in Applied Mathematics
Year
2011
ISBN-10
1611972000
ISBN-13
9781611972009
Format
Paperback
Publication Date
2011-12-08
Imprint
Society for Industrial & Applied Mathematics,U.S.
Place of Publication
New York
Country of Publication
United States
DEWEY
515.353
Illustrations
Illustrations
Media
Book
Short Title
TAYLOR APPROXIMATIONS FOR STOC
Language
English
Series Number
83
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