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

Arnaud Debussche (1, 2)

1 IPSO - Invariant Preserving SOlvers
2 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Mots clés: Weak order; stochastic heat equation; Euler scheme

Domaines: Analyse numérique [math.NA]; Probabilités [math.PR]

Arnaud Debussche. Weak approximation of stochastic partial differential equations: the non linear case. Mathematics of Computation, 2011, 80 (273), pp.89-117. ⟨hal-00271302⟩