Strong and weak order in averaging for SPDEs

Charles-Edouard Bréhier (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We show an averaging result for a system of stochastic evolution equations of parabolic type with slow and fast time scales. We derive explicit bounds for the approximation error with respect to the small parameter defining the fast time scale. We prove that the slow component of the solution of the system converges towards the solution of the averaged equation with an order of convergence is $1/2$ in a strong sense - approximation of trajectories - and $1$ in a weak sense - approximation of laws. These orders turn out to be the same as for the SDE case.

Mots clés: Stochastic Partial Differential Equations; Averaging Principle; Strong and Weak Approximation

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

Charles-Edouard Bréhier. Strong and weak order in averaging for SPDEs. Stochastic Processes and their Applications, 2012, 122 (7), pp.2553-2593. ⟨10.1016/j.spa.2012.04.007⟩. ⟨hal-00669457⟩