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

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 Added by Shiqiu Zheng
 Publication date 2018
  fields
and research's language is English




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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 $L^p(pgeq1)$ 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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