On pathwise uniqueness for stochastic heat equations with non-Lipschitz coefficients

• 成果类型: Article
• 署名作者: Mytnik, Leonid; Perkins, Edwin; Sturm, Anja
• 署名单位: Technion Israel Institute of Technology; University of British Columbia; University of Delaware
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000000331
• 发表日期: 2006
• 页码: 1910-1959
• 关键词: partial-differential equations

摘要

We consider the existence and pathwise uniqueness of the stochastic heat equation with a multiplicative colored noise term on R-d for d >= 1. We focus on the case of non-Lipschitz noise coefficients and singular spatial noise correlations. In the course of the proof a new result on Holder continuity of the solutions near zero is established.