THE BEHAVIOR OF SUPERPROCESSES NEAR EXTINCTION

• 成果类型: Article
• 署名作者: TRIBE, R
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989927
• 发表日期: 1992
• 页码: 286-311
• 关键词: partial-differential equations; super-brownian motion; DIFFUSIONS

摘要

In this paper we use a martingale problem characterization to study the behavior of finite measure valued superprocesses with a variety of spatial motions. In general the superprocess, when normalized to be a probability, will converge to a point mass at its extinction time. For some spatial motions we prove that there are times near extinction at which the closed support of the process is concentrated near one point. We obtain a Tanaka formula for the measure of a half space under a one dimensional symmetric stable superprocess of index a and we show this process fails to be a semimartingale if 1 < alpha < 2.