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

Shiqiu Zheng; Lidong Zhang; Lichao Feng

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arXiv · 1810.07086

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

Shiqiu Zheng·Lidong Zhang·Lichao Feng

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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 $L^p(p\geq1)$ 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.

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BibTeX RIS

Shiqiu Zheng, Lidong Zhang, Lichao Feng. 2018-10-16. On the backward stochastic differential equation with generator $f(y)|z|^2$. https://arxiv.org/abs/1810.07086

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