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The current investigation aims to study the stochastic homogenization for afamily of functionals with convex and nonstandard growth integrands defined onOrlicz-Sobolev's spaces. It focuses on the concept of stochastic two-scaleconvergence, which is a combinaison of both well-know two-scale convergence andstochastic two-scale convergence in the mean schemes. One fundamental in thistopic is to extend the classical compactness results of the stochastictwo-scale convergence method to this type of spaces.

Stochastic two-scale convergence in Orlicz-Sobolev's spaces and applications to the homogenization of an integral functional