Uniqueness for a class of one-dimensional stochastic PDEs using moment duality

• 成果类型: Article
• 署名作者: Athreya, S; Tribe, R
• 署名单位: University of British Columbia; University of Warwick
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2000
• 页码: 1711-1734
• 关键词: partial-differential equations; heat-equation; noise

摘要

We establish a duality relation for the moments of bounded solutions to a class of one-dimensional parabolic stochastic partial differential equations. The equations are driven by multiplicative space-time white noise, with a non-Lipschitz multiplicative functional. The dual process is a system of branching Brownian particles. The same method can be applied to show uniqueness in law for a class of non-Lipschitz finite dimensional stochastic differential equations.