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Taylor approximations for stochastic partial differential equations
Tag	Description
020	$a978-1-611972-01-6
082	$a515.353 (DDC 22)
099	$aOnline Resource : Society for Industrial and Applied Mathematics
100	$aJentzen, Arnulf.
245	$aTaylor approximations for stochastic partial differential equations$h[Ebook]$cArnulf Jentzen, Peter E. Kloeden.
260	$aPhiladelphia, Pa.$bSociety for Industrial and Applied Mathematics$c2011.
300	$a1 online resource (xiv, 211 pages)
440	$aCBMS-NSF regional conference series in applied mathematics$v83
505	$aChapter 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.
520	$aThis 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.
533	$aDigital reproduction.$bPhiladelphia :$cSociety for Industrial and Applied Mathematics,$d2011.$fCBMS-NSF Regional Conference Series in Applied Mathematics$nPDF files ; Access available with World Wide Web only for internal SISSA users ; access through IP
538	$aMode of access: World Wide Web. System requirements: Adobe Acrobat Reader.
700	$aKloeden, Peter E.
710	$aSociety for Industrial and Applied Mathematics
830	$aCBMS-NSF regional conference series in applied mathematics ;$v83.-
856	$uhttp://dx.doi.org/10.1137/1.9781611972016