Ordered random walks with heavy tails

2011/03/23 by Denis Denisov, Denisov, Denis, Vitali Wachtel +1
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60F17 #msc:60G40 #msc:60G50

paper · pdf · doi:10.48550/arxiv.1103.4529

20 pages

arxiv created 2011/03/23 · arxiv updated 2011/03/24

Abstract

This note continues paper of Denisov and Wachtel (2010), where we have constructed a k-dimensional random walk conditioned to stay in the Weyl chamber of type A. The construction was done under the assumption that the original random walk has k-1 moments. In this note we continue the study of killed random walks in the Weyl chamber, and assume that the tail of increments is regularly varying of index α<k-1. It appears that the asymptotic behaviour of random walks is different in this case. We determine the asymptotic behaviour of the exit time, and, using thisinformation, construct a conditioned process which lives on a partial compactification of the Weyl chamber.

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