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 |
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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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