Super-Brownian motion with reflecting historical paths

• 成果类型: Article
• 署名作者: Burdzy, K; Le Gall, JF
• 署名单位: University of Washington; University of Washington Seattle; Universite PSL; Ecole Normale Superieure (ENS)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s004400100157
• 发表日期: 2001
• 页码: 447-491
• 关键词: partial-differential equations; DIFFUSIONS

摘要

We consider super-Brownian motion whose historical paths reflect from each other. unlike those of the usual historical super-Brownian motion. We prove tightness for the family of distributions corresponding to a sequence of discrete approximations but we leave the problem of uniqueness of the limit open. We prove a few results about path behavior for processes under any limit distribution. In particular, we show that for any gamma > 0, a typical increment of a reflecting historical path over a small time interval At is not greater than (Deltat)(3/4-gamma).