In this paper we discuss the concept of stochastic two-scale convergence, which is appropriate to solve coupledperiodic
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.