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Ordered random walks with heavy tails

Denisov, Denis and Wachtel, Vitali 2012. Ordered random walks with heavy tails. Electronic Journal of Probability 17 , pp. 1-21. 10.1214/EJP.v17-1719

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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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Institute of Mathematical Statistics
ISSN: 1083-6489
Date of First Compliant Deposit: 30 March 2016
Last Modified: 23 May 2023 15:33
URI: https://orca.cardiff.ac.uk/id/eprint/17456

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