The Annals of Probability

Stable Processes on the Boundary of a Regular Tree

Phillippe Marchal

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Abstract

We define a class of processes on the boundary of a regular tree that can be viewed as “stable” Lévy processes on $(\mathbb{Z}/n_0\mathbb{Z})^\mathbb{N}$. 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 in finite multiplicity when the index of the process equals the dimension of the state space, as for planar Brownian motion.

Article information

Source
Ann. Probab., Volume 29, Number 4 (2001), 1591-1611.

Dates
First available in Project Euclid: 5 March 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1015345763

Digital Object Identifier
doi:10.1214/aop/1015345763

Mathematical Reviews number (MathSciNet)
MR1880233

Zentralblatt MATH identifier
1016.60056

Citation

Marchal, Phillippe. Stable Processes on the Boundary of a Regular Tree. Ann. Probab. 29 (2001), no. 4, 1591--1611. doi:10.1214/aop/1015345763. https://projecteuclid.org/euclid.aop/1015345763


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  • CNRS, DMA, ´Ecole Normale Sup´erieure 45 rue d'Ulm 75230 Paris cedex 05 France E-mail: marchal@dmi.ens.fr