On the backward stochastic differential equation with generator f(y)|z|2

Abstract

In this paper, we consider the backward stochastic differential equation (BSDE) with generator f(y)|z|2, where the function f is defined on an open interval D and locally integrable. The existence and uniqueness of bounded solutions and Lp(p≥1) solutions of such BSDEs are obtained. Some comparison theorems and a converse comparison theorem of such BSDEs are established. As an application, we give a probabilistic interpretation of viscosity solution of quadratic PDEs.