Taylor Approximations for Stochastic Partial Differential Equations - Arnulf Jentzen
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Présentation Taylor Approximations For Stochastic Partial Differential Equations de Arnulf Jentzen Format Broché
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Résumé :
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 Hö...
Biographie:
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.
Sommaire:
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....