Stable processes on the boundary of a regular tree

• 成果类型: Article
• 署名作者: Marchal, P
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1015345763
• 发表日期: 2001
• 页码: 1591-1611
• 关键词: markov-processes; brownian-motion; Levy processes; random-walks; capacity; points; polar; times; sets

摘要

We define a class of processes on the boundary of a regular tree that can be viewed as stable Levy processes on (Z/n(0)Z)(N). We show that the range of these processes can be compared with a Bernoulli percolation as in Peres which easily leads to various results on the intersection properties. We develop an alternative approach based on the comparison with a branching random walk. By this method we establish the existence of points of infinite multiplicity when the index of the process equals the dimension of the state space, as for planar Brownian motion.