A stochastic log-laplace equation

• 成果类型: Article
• 署名作者: Xiong, J
• 署名单位: University of Tennessee System; University of Tennessee Knoxville
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000000540
• 发表日期: 2004
• 页码: 2362-2388
• 关键词: superprocesses

摘要

We study a nonlinear stochastic partial differential equation whose solution is the conditional log-Laplace functional of a superprocess in a random environment. We establish its existence and uniqueness by smoothing out the nonlinear term and making use of the particle system representation developed by Kurtz and Xiong [Stochastic Process. Appl. 83 (1999) 103-126]. We also derive the Wong-Zakai type approximation for this equation. As an application, we give a direct proof of the moment formulas of Skoulakis and Adler [Ann. Appl. Probab. 11 (2001) 488-543].