Maximum principle for quasi-linear reflected backward SPDEs

Guanxing Fu, Ulrich Horst, Jinniao Qiu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)

Abstract

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 non-zero 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.

Original languageEnglish
Pages (from-to)307-336
Number of pages30
JournalJournal of Mathematical Analysis and Applications
Volume456
Issue number1
DOIs
Publication statusPublished - 1 Dec 2017

Keywords

  • Backward stochastic partial differential equation
  • De Giorgi's iteration
  • Maximum principle
  • Reflected backward stochastic partial differential equation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this