Weak approximation of stochastic partial differential equations: the non linear case
Numerical Analysis
2008-12-18 v1 Probability
Abstract
We study the error of the Euler scheme applied to a stochastic partial differential equation. We prove that as it 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 a semilinear stochastic heat equation driven by a space-time white noise.
Keywords
Cite
@article{arxiv.0804.1304,
title = {Weak approximation of stochastic partial differential equations: the non linear case},
author = {Arnaud Debussche},
journal= {arXiv preprint arXiv:0804.1304},
year = {2008}
}