LATTICE APPROXIMATIONS OF REFLECTED STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS DRIVEN BY SPACE-TIME WHITE NOISE

• 成果类型: Article
• 署名作者: Zhang, Tusheng
• 署名单位: University of Manchester
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/16-AAP1186
• 发表日期: 2016
• 页码: 3602-3629
• 关键词: dependent domains; spdes; integration; BOUNDARY; motion; sdes

摘要

We introduce a discretization/approximation scheme for reflected stochastic partial differential equations driven by space time white noise through systems of reflecting stochastic differential equations. To establish the convergence of the scheme, we study the existence and uniqueness of solutions of Skorohod-type deterministic systems on time-dependent domains. We also need to establish the convergence of an approximation scheme for deterministic parabolic obstacle problems. Both are of independent interest on their own.