Occupation time large deviations for critical, branching Brownian motion, super-Brownian motion and related processes

• 成果类型: Article
• 署名作者: Deuschel, JD; Rosen, J
• 署名单位: Technical University of Berlin; City University of New York (CUNY) System; College of Staten Island (CUNY)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1998
• 页码: 602-643
• 关键词: superprocesses

摘要

We derive a large deviation principle for the occupation time functional, acting on functions with zero Lebesgue integral, for both super-Brownian motion and critical branching Brownian motion in three dimensions. Our technique, based on a moment formula of Dynkin, allows us to compute the exact rate functions, which differ for the two processes. Obtaining the exact rate function for the super-Brownian motion solves a conjecture of Lee and Remillard. We also show the corresponding CLT and obtain similar results for the superprocesses and critical branching process built over the symmetric stable process of index beta in R-d, with d < 2 beta < 2 + d.