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Weak approximation of stochastic partial differential equations: the nonlinear case


Author: Arnaud Debussche
Journal: Math. Comp. 80 (2011), 89-117
MSC (2010): Primary 65M15, 65C30, 60H15, 60H35
DOI: https://doi.org/10.1090/S0025-5718-2010-02395-6
Published electronically: August 16, 2010
MathSciNet review: 2728973
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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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Additional Information

Arnaud Debussche
Affiliation: IRMAR, ENS Cachan Bretagne, CNRS, UEB, av Robert Schuman, F-35170 Bruz, France
Email: arnaud.debussche@bretagne.ens-cachan.fr

DOI: https://doi.org/10.1090/S0025-5718-2010-02395-6
Keywords: Weak order, stochastic heat equation, Euler scheme.
Received by editor(s): June 6, 2008
Received by editor(s) in revised form: July 20, 2009
Published electronically: August 16, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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