THE OBSTACLE PROBLEM FOR QUASILINEAR STOCHASTIC PDES: ANALYTICAL APPROACH

• 成果类型: Article
• 署名作者: Denis, Laurent; Matoussi, Anis; Zhang, Jing
• 署名单位: Universite Paris Saclay; Le Mans Universite; Institut Polytechnique de Paris; Ecole Polytechnique
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/12-AOP805
• 发表日期: 2014
• 页码: 865-905
• 关键词: partial-differential-equations; spdes; reflection

摘要

We prove an existence and uniqueness result for quasilinear Stochastic PDEs with obstacle (OSPDE in short). Our method is based on analytical technics coming from the parabolic potential theory. The solution is expressed as a pair (u, v) where u is a predictable continuous process which takes values in a proper Sobolev space and v is a random regular measure satisfying the minimal Skohorod condition.