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

Shiqiu Zheng; Lidong Zhang; Lichao Feng

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

Probability 2021-03-04 v5

Authors: Shiqiu Zheng , Lidong Zhang , Lichao Feng

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.

Keywords

backward stochastic differential equations generator f(y)|z|^2 comparison theorem viscosity solution quadratic pdes local integrability

Cite

@article{arxiv.1810.07086,
  title  = {On the backward stochastic differential equation with generator $f(y)|z|^2$},
  author = {Shiqiu Zheng and Lidong Zhang and Lichao Feng},
  journal= {arXiv preprint arXiv:1810.07086},
  year   = {2021}
}

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20 pages, final version

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

Abstract

Keywords

Cite

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