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 m...

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Bibliographische Detailangaben

Hauptverfasser:	Jentzen, Arnulf 1983- (VerfasserIn), Kloeden, Peter E. 1949- (VerfasserIn)
Format:	Elektronisch E-Book
Sprache:	English
Veröffentlicht:	Philadelphia, Pa. Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104) 2011
Schriftenreihe:	CBMS-NSF regional conference series in applied mathematics 83
Schlagworte:	Stochastic partial differential equations Approximation theory Stochastische partielle Differentialgleichung Numerisches Verfahren Approximation
Online-Zugang:	TUM01 UBW01 UBY01 UER01 Volltext
Zusammenfassung:	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 H lder 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
Beschreibung:	1 Online-Ressource (xiv, 220 Seiten) Illustrationen
ISBN:	9781611972016
DOI:	10.1137/1.9781611972016