Open Access
April, 1992 Polar and Nonpolar Sets for a Tree Indexed Process
Steven N. Evans
Ann. Probab. 20(2): 579-590 (April, 1992). DOI: 10.1214/aop/1176989792


We consider a class of stochastic processes of a type that was first introduced by Dubins and Freedman. These processes are indexed by the lines of descent through an infinite tree and take values in a space of sequences. Our main results concern necessary and sufficient conditions of a potential theoretic type for a subset of the state-space to be hit with positive probability by the sample paths of the process. We examine these conditions in some specific examples and also relate them to conditions expressed in terms of Hausdorff dimension. As well, we use similar techniques to investigate multiple points in the sample paths of the process.


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Steven N. Evans. "Polar and Nonpolar Sets for a Tree Indexed Process." Ann. Probab. 20 (2) 579 - 590, April, 1992.


Published: April, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0757.60070
MathSciNet: MR1159560
Digital Object Identifier: 10.1214/aop/1176989792

Primary: 60J45
Secondary: 60B99 , 60G10 , 60G17

Keywords: capacity , energy , Hausdorff dimension , path intersections , polar set , stochastic process on a group , tree

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.20 • No. 2 • April, 1992
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