Weak approximation of stochastic partial differential equations: the nonlinear case

Debussche, Arnaud

doi:10.1090/S0025-5718-2010-02395-6

Weak approximation of stochastic partial differential equations: the nonlinear case
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by Arnaud Debussche;

Math. Comp. 80 (2011), 89-117

DOI: https://doi.org/10.1090/S0025-5718-2010-02395-6

Published electronically: August 16, 2010

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Abstract:

We study the error of the Euler scheme applied to a stochastic partial differential equation. We prove that, as is often the case, the weak order of convergence is twice the strong order. A key ingredient in our proof is Malliavin calculus which enables us to get rid of the irregular terms of the error. We apply our method to the case of a semilinear stochastic heat equation driven by a space-time white noise.

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