Maximum Principle for Quasi-linear Backward Stochastic Partial Differential Equations
Probability
2011-03-08 v1
Abstract
In this paper we are concerned with the maximum principle for quasi-linear backward stochastic partial differential equations (BSPDEs for short) of parabolic type. We first prove the existence and uniqueness of the weak solution to quasi-linear BSPDE with the null Dirichlet condition on the lateral boundary. Then using the De Giorgi iteration scheme, we establish the maximum estimates and the global maximum principle for quasi-linear BSPDEs. To study the local regularity of weak solutions, we also prove a local maximum principle for the backward stochastic parabolic De Giorgi class.
Keywords
Cite
@article{arxiv.1103.1038,
title = {Maximum Principle for Quasi-linear Backward Stochastic Partial Differential Equations},
author = {Jinniao Qiu and Shanjian Tang},
journal= {arXiv preprint arXiv:1103.1038},
year = {2011}
}