Path properties of superprocesses with a general branching mechanism

• 成果类型: Article
• 署名作者: Delmas, JF
• 署名单位: Institut Polytechnique de Paris; Ecole des Ponts ParisTech
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1022677441
• 发表日期: 1999
• 页码: 1099-1134
• 关键词: super-brownian-motion; connected components; closed support

摘要

We first consider a super Brownian motion X with a general branching mechanism. Using the Brownian snake representation with subordination, we get the Hausdorff dimension of supp X-t, the topological support of X-t and, more generally, the Hausdorff dimension of U-t is an element of B supp X-t. We also provide estimations on the hitting probability of small balls for those random measures. We then deduce that the support is totally disconnected in high dimension. Eventually, considering a super alpha-stable process with a general branching mechanism, we prove that in low dimension this random measure is absolutely continuous with respect to the Lebesgue measure.