A Stochastic Representation for Fully Nonlinear PDEs and Its Application to Homogenization
Naoyuki Ichihara · Institutional Repositories DataBase (IRDB) · 2005
Abstract. We establish a stochastic representation formula for solutions to fully nonlinear second-order partial differential equations of parabolic type. For this purpose, we introduce forward-backward stochastic differential equations with random coefficients. We next apply them to homogenization of fully nonlinear parabolic equations. As a byproduct, we obtain an estimate concerning the convergence rate of solutions. The results partially generalize homogenization of Hamilton-Jacobi-Bellman equations studied by R. Buckdahn and the author.