Weak solution for a class of fully nonlinear stochastic Hamilton-Jacobi-Bellman equations

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:127

Article

Qiu, Jinniao¹ 

[1] Univ Michigan, Dept Math, 530 Church St, Ann Arbor, MI 48109 USA

关键词: Stochastic Hamilton-Jacobi-Bellman equation;    Backward stochastic partial differential equation;    Weak solution;    Non-Markovian control;    Potential;   

DOI  :  10.1016/j.spa.2016.09.010

来源: Elsevier

【 摘 要 】

This paper is concerned with a class of stochastic Hamilton-Jacobi-Bellman equations with controlled leading coefficients, which are fully nonlinear backward stochastic partial differential equations (BSPDEs for short). In order to formulate the weak solution for such kind of BSPDEs, a class of regular random parabolic potentials are introduced in the backward stochastic framework. The existence and uniqueness of weak solution is proved, and for the partially non-Markovian case, we obtain the associated gradient estimate. As a byproduct, the existence and uniqueness of solution for a class of degenerate reflected BSPDEs is discussed as well. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free