Stochastic two-scale convergence of an integral functional

Abstract

In this paper we discuss the concept of stochastic two-scale convergence, which is appropriate to solve coupled-periodic and stochastic homogenization problems. This concept is a combination of both well-known two-scale convergence and stochastic two-scale convergence in the mean schemes, and is a generalization of the said previous methods. By way of illustration we apply it to solve a homogenization problem related to an integral functional with convex integrand. This problematic relies on the notion of dynamical system which is our basic tool.