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The exponential integrator scheme for stochastic partial differential equations: Pathwise error bounds

✍ Scribed by P.E. Kloeden; G.J. Lord; A. Neuenkirch; T. Shardlow

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
519 KB
Volume
235
Category
Article
ISSN
0377-0427

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✦ Synopsis

We present an error analysis for the pathwise approximation of a general semilinear stochastic evolution equation in d dimensions. We discretise in space by a Galerkin method and in time by using a stochastic exponential integrator. We show that for spatially regular (smooth) noise the number of nodes needed for the noise can be reduced and that the rate of convergence degrades as the regularity of the noise reduces (and the noise becomes rougher).

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✍ Vlad Bally; Denis Talay πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 304 KB

We study the approximation problem of Ef(Xr) by Ef(X~.), where (Xt) is the solution of a stochastic differential equation, (X~) is defined by the Euler discretization scheme with step T/n, and f is a given function. For smooth f's, Talay and Tubaro had shown that the error Ef(Xr) -Ef(X~) can be expa