Maximum principle for quasi-linear reflected backward SPDEs

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:456

Article

Fu, Guanxing¹  Horst, Ulrich¹  Qiu, Jinniao² 

[1] Humboldt Univ, Dept Math, Unter Linden 6, D-10099 Berlin, Germany

[2] Univ Calgary, Dept Math & Stat, 2500 Univ Dr, Calgary, AB T2N 1N4, Canada

关键词: Reflected backward stochastic partial differential equation;    Backward stochastic partial differential equation;    Maximum principle;    De Giorgi's iteration;   

DOI  :  10.1016/j.jmaa.2017.06.047

来源: Elsevier

【 摘 要 】

This paper establishes a maximum principle for quasi-linear reflected backward stochastic partial differential equations (RBSPDEs for short). We prove the existence and uniqueness of the weak solution to RBSPDEs allowing for nonzero Dirichlet boundary conditions and, using a stochastic version of De Giorgi's iteration, establish the maximum principle for RBSPDEs on a general domain. The maximum principle for RBSPDEs on a bounded domain and the maximum principle for backward stochastic partial differential equations (BSPDEs for short) on a general domain can be obtained as byproducts. Finally, the local behavior of the weak solutions is considered. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free