Taylor Approximations for Stochastic Partial Differential Equations

Taylor Approximations for Stochastic Partial Differential Equations

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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 ordinar...