Electronic Journal of Probability

Ordered random walks with heavy tails

Denis Denisov and Vitali Wachtel

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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.

Article information

Source
Electron. J. Probab. Volume 17 (2012), paper no. 4, 21 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465062326

Digital Object Identifier
doi:10.1214/EJP.v17-1719

Mathematical Reviews number (MathSciNet)
MR2878783

Zentralblatt MATH identifier
1246.60069

Subjects
Primary: 60G50: Sums of independent random variables; random walks

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

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Denisov, Denis; Wachtel, Vitali. Ordered random walks with heavy tails. Electron. J. Probab. 17 (2012), paper no. 4, 21 pp. doi:10.1214/EJP.v17-1719. https://projecteuclid.org/euclid.ejp/1465062326


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