Quantitative Homogenization of PDEs with Neumann boundary conditions: a probabilistic approach

Abstract

In this paper, we study quantitative homogenization for viscosity solutions of multi-scale semilinear second order partial differential equations (PDEs) on convex domains with Neumann boundary conditions. To this aim we use the probabilistic approach by studying the quantitative homogenization of backward stochastic differential equations (SDEs) associated with slow-fast systems of reflected SDEs.