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2012 Ordered random walks with heavy tails
Denis Denisov, Vitali Wachtel
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Electron. J. Probab. 17: 1-21 (2012). DOI: 10.1214/EJP.v17-1719

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 $\alpha<k-1$. 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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Denis Denisov. Vitali Wachtel. "Ordered random walks with heavy tails." Electron. J. Probab. 17 1 - 21, 2012. https://doi.org/10.1214/EJP.v17-1719

Information

Accepted: 11 January 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1246.60069
MathSciNet: MR2878783
Digital Object Identifier: 10.1214/EJP.v17-1719

Subjects:
Primary: 60G50

Keywords: Doob $h$-transform , Dyson's Brownian motion , Martin boundary , superharmonic function , Weyl chamber

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