Weak approximation of stochastic partial differential equations: the non linear case

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.

References in corpus (1)

• On implicit and explicit discretization schemes for parabolic SPDEs in any dimension

Cited by in corpus (1)

• Weak convergence for the stochastic heat equation driven by Gaussian white noise