Geometric aspects of Fleming-Viot and Dawson-Watanabe processes

• 成果类型: Article
• 署名作者: Schied, A
• 署名单位: Humboldt University of Berlin
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1997
• 页码: 1160-1179
• 关键词: large deviations

摘要

This paper is concerned with the intrinsic metrics of the two main classes of superprocesses. For the Fleming-Viot process, we identify it as the Bhattacharya distance, and for Dawson-Watanabe processes, we find the Kakutani-Hellinger metric. The corresponding geometries are studied in some detail. In particular, representation formulas for geodesics and are length functionals are obtained. The relations between the two metrics yield a geometric interpretation of the identification of the Fleming-Viot process as a Dawson-Watanabe superprocess conditioned to have total mass 1. As an application, a functional limit theorem for super-Brownian motion conditioned on local extinction is proved.