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October 2001 Stable Processes on the Boundary of a Regular Tree
Phillippe Marchal
Ann. Probab. 29(4): 1591-1611 (October 2001). DOI: 10.1214/aop/1015345763


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.


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Phillippe Marchal. "Stable Processes on the Boundary of a Regular Tree." Ann. Probab. 29 (4) 1591 - 1611, October 2001.


Published: October 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1016.60056
MathSciNet: MR1880233
Digital Object Identifier: 10.1214/aop/1015345763

Rights: Copyright © 2001 Institute of Mathematical Statistics

Vol.29 • No. 4 • October 2001
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