Backward stochastic differential equations and quasilinear partial differential equations

Abstract

: In this paper we first review the classical Feynman-Kac formula and then introduce its generalization obtained by Pardoux-Peng via backward stochastic differential equations. It is because of the usefulness of the Feynman-Kac formula in the study of parabolic partial differential equations we see clearly how worthy to study the backward stochastic differential equations in more detail. We hence further review the work of Pardoux and Peng on backward stochastic differential equations and establish a new theorem on the existence and uniqueness of the adapted solution to a backward stochastic differential equation under a weaker condition than Lipschitz one.Key Words: Backward stochastic differential equation, parabolic partial differential equation, adapted solution, Bihari's inequality.