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

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 obtain...

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Bibliographic Details
Published in:arXiv.org 2021-03
Main Authors: Zheng, Shiqiu, Zhang, Lidong, Feng, Lichao
Format: Article
Language:English
Subjects:
Differential equations
Theorems
Online Access:Get full text
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Summary: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.
ISSN:2331-8422