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 Holder
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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