Localization errors in solving stochastic partial differential equations in the whole space

Gerencsér, Máté; Gyöngy, István

doi:10.1090/mcom/3201

Localization errors in solving stochastic partial differential equations in the whole space
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by Máté Gerencsér and István Gyöngy PDF

Math. Comp. 86 (2017), 2373-2397 Request permission

Abstract:

Cauchy problems with SPDEs on the whole space are localized to Cauchy problems on a ball of radius $R$. This localization reduces various kinds of spatial approximation schemes to finite dimensional problems. The error is shown to be exponentially small. As an application, a numerical scheme is presented which combines the localization and the space and time discretization, and thus is fully implementable.

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