A Tartar approach to periodic homogenization of linear hyperbolic stochastic partial differential equation

Abstract

This paper deals with the homogenization of a linear hyperbolic stochastic partial differential equation (SPDE) with highly oscillating periodic coefficients. We use Tartar’s method of oscillating test functions and deep probabilistic compactness results due to Prokhorov and Skorokhod. We show that the sequence of solutions of the original problem converges in suitable topologies to the solution of a homogenized linear hyperbolic SPDE with constant coefficients. We also prove the convergence of the associated energies.