Homogenization for stochastic partial differential equations derived from nonlinear filterings with feedback

Abstract

We discuss the homogenization of stochastic partial differential equations whose coefficients are rapidly oscillating and are perturbed by a diffusion process. Such class of equations appear in nonlinear filtering problems with feedback. We specify the constant coefficients of the limit equation. The constants are essentially different from the case where the coefficients do not contain perturbed factors.