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Field name	Details
Dewey Class	515.353 (DDC 22)
Title	Taylor approximations for stochastic partial differential equatio ([Ebook] / Arnulf Jentzen, Peter E. Kloeden.
Author	Jentzen, Arnulf
Added Personal Name	Kloeden, Peter E.
Other name(s)	Society for Industrial and Applied Mathematics
Publication	Philadelphia, P : Society for Industrial and Applied Mathemati , 2011.
Physical Details	1 online resource (xiv, 211 pages)
Series	CBMS-NSF regional conference series in applied mathemati ; 83
ISBN	978-1-611972-01-6
Summary Note	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{under}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.:
Contents note	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.
Mode of acces to digital resource	Digital reproduction. Philadelphia : Society for Industrial and Applied Mathematics, 2011. PDF files ; Access available with World Wide Web only for internal SISSA users ; access through IP
System details note	Mode of access: World Wide Web. System requirements: Adobe Acrobat Reader.
Internet Site	http://dx.doi.org/10.1137/1.9781611972016
Links to Related Works	Subject References: Stochastic partial differential equations. Approximation theory . Authors: Jentzen, Arnulf . Kloeden, Peter E. . Corporate Authors: Society for Industrial and Applied Mathematics . Series: CBMS-NSF Regional Conference Series in Applied Mathematics . Classification: 515.353 (DDC 22) .

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Taylor approximations for stochastic partial differential equations

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