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.
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