Taylor Approximations for Stochastic Partial Differential Equations

Language: English

Published by Society for Industrial and Applied Mathematics,U.S., US, 2011

1611972000 / 9781611972009

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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.

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Title
Taylor Approximations for Stochastic Partial Differential Equations
Author
Arnulf Jentzen, Peter E. Kloeden
Publisher
Society for Industrial and Applied Mathematics,U.S., US
Publication year
2011
Condition
New
Binding
Paperback
Language
English
ISBN 10
1611972000
ISBN 13
9781611972009
Item weight
390 grams

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