Homogenization of a stochastic nonlinear reaction-diffusion equation with a large reaction term: The almost periodic framework

Homogenization of a stochastic nonlinear reaction-diffusion equation with a large nonlinear term is considered. Under a general Besicovitch almost periodicity assumption on the coefficients of the equation we prove that the sequence of solutions of the said problem converges in probability towards the solution of a rather different type of equation, namely, the stochastic nonlinear convection-diffusion equation which we explicitly derive in terms of appropriate functionals. We study some particular cases such as the periodic framework, and many others. This is achieved under a suitable generalized concept of Σ-convergence for stochastic processes.