Homogenization of Linear and Semilinear Second Order Parabolic PDEs with Periodic Coefficients: A Probabilistic Approach

Abstract

We study the limit of the solution of linear and semilinear second order PDEs of parabolic type, with rapidly oscillating periodic coefficients, singular drift, and singular coefficient of the zeroth order term. Our method of proof is fully probabilistic and builds upon the arguments in earlier work. In the linear case, we use the Feynman Kac formula to represent the solution of the parabolic PDE, and in the semilinear case we use an associated backward stochastic differential equation.