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Regenerative compositions in the case of slow variation: A renewal theory approach


 
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1. Title Title of document Regenerative compositions in the case of slow variation: A renewal theory approach
 
2. Creator Author's name, affiliation, country Alexander Gnedin; Queen Mary University of London; United Kingdom
 
2. Creator Author's name, affiliation, country Alexander Iksanov; National T. Shevchenko University of Kiev; Ukraine
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) first passage time; number of blocks; regenerative composition; renewal theory; weak convergence
 
3. Subject Subject classification 60F05; 60K05; 60C05
 
4. Description Abstract

A regenerative composition structure is a sequence of ordered partitions derived from the range of a subordinator by a natural sampling procedure. In this paper, we extend previous studies on the asymptotics of the number of blocks $K_n$ in the composition of integer $n$, in the case when the Lévy measure of the subordinator has a property of slow variation at $0$. Using tools from the renewal theory the limit laws for $K_n$ are obtained in terms of integrals involving the Brownian motion or stable processes. In other words, the limit laws are either normal or other stable distributions, depending on the behavior of the tail of Lévy measure at $\infty$. Similar results are also derived for the number of singleton blocks.
 
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7. Date (YYYY-MM-DD) 2012-09-17
 
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/2002
 
10. Identifier Digital Object Identifier 10.1214/EJP.v17-2002
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 17
 
12. Language English=en en
 
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