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