Weak order in averaging principle for stochastic wave equation with a fast oscillation

This article deals with the weak error in averaging principle for a stochastic wave equation on a bounded interval [0,L], perturbed by an oscillating term arising as the solution of a stochastic reaction-diffusion equation evolving on the fast time scale. Under suitable conditions, it is proved that the rate of weak convergence of the original solution to the solution of the corresponding averaged equation is of order 1 via an asymptotic expansion approach.