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.
Citation
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
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