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Ordered random walks with heavy tails


 
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1. Title Title of document Ordered random walks with heavy tails
 
2. Creator Author's name, affiliation, country Denis E Denisov; Cardiff University; United Kingdom
 
2. Creator Author's name, affiliation, country Vitali Wachtel; University of Munich; Germany
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Dyson's Brownian Motion; Doob $h$-transform; superharmonic function; Weyl chamber; Martin boundary
 
3. Subject Subject classification 60G50
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) DFG
 
7. Date (YYYY-MM-DD) 2012-01-11
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/1719
 
10. Identifier Digital Object Identifier 10.1214/EJP.v17-1719
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 17
 
12. Language English=en en
 
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