Some properties of the range of super-Brownian motion

• 成果类型: Article
• 署名作者: Delmas, JF
• 署名单位: Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s004400050233
• 发表日期: 1999
• 页码: 505-547
• 关键词: superprocesses; trees

摘要

We consider a super-Brownian motion X. Its canonical measures can be studied through the path-valued process called the Brownian snake. We obtain the limiting behavior of the volume of the epsilon-neighborhood for the range of the Brownian snake, and as a consequence we derive the analogous result for the range of super-Brownian motion and for the support of the integrated super-Brownian excursion. Then we prove the support of X-t is capacity-equivalent to [0, 1](2) in R-d, d greater than or equal to 3, and the range of X, as well as the support of the integrated super-Brownian excursion are capacity-equivalent to [0, 1](4) in R-d, d greater than or equal to 5.