Abstract:
In this article, we show that the concept of sigma-convergence associated to
stochastic processes can tackle the homogenization of stochastic partial differential
equations. In this regard, the homogenization of a stochastic nonlinear partial
differential equation is addressed. Using some deep compactness results such as
the Prokhorov and Skorokhod theorems, we prove that the sequence of solutions of
this problem converges in probability towards the solution of an equation of the
same type. To proceed with, we use the concept of sigma-convergence for stochastic
processes, which takes into account both the deterministic and random behaviours
of the solutions of the problem.
