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.