Electronic Journal of Probability
- Electron. J. Probab.
- Volume 17 (2012), paper no. 4, 21 pp.
Ordered random walks with heavy tails
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.
Electron. J. Probab. Volume 17 (2012), paper no. 4, 21 pp.
Accepted: 11 January 2012
First available in Project Euclid: 4 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G50: Sums of independent random variables; random walks
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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