Taylor Approximations for Stochastic Partial Differential Equations

Häftad, Engelska, 2011

Del i serien CBMS-NSF Regional Conference Series in Applied Mathematics

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2011-11-30
Mått:172 x 248 x 15 mm
Vikt:393 g
Format:Häftad
Språk:Engelska
Serie:CBMS-NSF Regional Conference Series in Applied Mathematics
Antal sidor:234
Förlag:Society for Industrial & Applied Mathematics,U.S.
ISBN:9781611972009

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Mer om författaren

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.

Innehållsförteckning

PrefaceList of FiguresChapter 1: IntroductionPart I: Random and Stochastic Ordinary Partial Differential EquationsChapter 2: RODEsChapter 3: SODEsChapter 4: SODEs with Nonstandard AssumptionsPart II: Stochastic Partial Differential EquationsChapter 5: SPDEsChapter 6: Numerical Methods for SPDEsChapter 7: Taylor Approximations for SPDEs with Additive NoiseChapter 8: Taylor Approximations for SPDEs with Multiplicative NoiseAppendix: Regularity Estimates for SPDEsBibliographyIndex.