Stability of BSDEs with Random Terminal Time and Homogenization of Semilinear Elliptic PDEs

In this paper, we extend the probabilistic method for homogenization of semi-linear parabolic PDEs, developed by Buckdahn, Hu, and Peng to the case of elliptic PDEs. First, we give a stability result for BSDEs with random terminal time which are related to elliptic PDEs as shown in Peng (Stochastics Stochastics Rep.37(1991), 61–74). In the one dimensional case, we also partially relax the monotonicity assumption on the coefficient. Then, we use these stability results for BSDEs with random terminal time to study homogenization of systems of semilinear elliptic PDEs.