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On the backward stochastic differential equation with generator $f(y)|z|^2$ (1810.07086v5)
Published 16 Oct 2018 in math.PR
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 $Lp(p\geq1)$ 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.