Ordered random walks with heavy tails

Denis E Denisov (Cardiff University)
Vitali Wachtel (University of Munich)


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 $\alpha<k-1$. 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 this information, construct a conditioned process which lives on a partial compactification of the Weyl chamber.

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Pages: 1-21

Publication Date: January 11, 2012

DOI: 10.1214/EJP.v17-1719


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