| Título: | Ordered random walks with heavy tails |
| Autores: |
Denisov, Denis E; Cardiff University Wachtel, Vitali; University of Munich |
| Fecha: | 2012-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: | Peer-reviewed Article |
| Tema: |
Dyson's Brownian Motion; Doob $h$-transform; superharmonic function; Weyl chamber; Martin boundary 60G50 |
| Descripción: | 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. |
| Idioma: | Inglés |
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