The obstacle problem for quasilinear stochastic integral-partial differential equations. Issue 2 (17th February 2020)

• Record Type: Journal Article
• Authors: Dong, Yuchao; Yang, Xue; Zhang, Jing
• Is Part Of: Stochastics. Volume 92:Issue 2(2020)
• Page Start: 297
• Page End: 333
• Publication Date: 2020-02-17
• Subjects: Stochastic partial differential equations -- integral-partial differential operators -- obstacle problem -- backward doubly stochastic differential equations with jumps -- regular potential -- regular measure; Primary 60H15 -- 60G46 -- 35R60; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2019.1624751
• Languages: English
• ISSNs: 1744-2508

Abstract

ABSTRACT: We prove the existence and uniqueness of solutions to a kind of quasilinear stochastic integral-partial differential equations with obstacles. Our method is based on the probabilistic interpretation of the solutions so that penalization method can be applied to a sequence of backward doubly stochastic differential equations with jumps. Relations between regular potentials and regular measures play an important role.