Open Access
Translator Disclaimer
2012 Regenerative compositions in the case of slow variation: A renewal theory approach
Alexander Gnedin, Alexander Iksanov
Author Affiliations +
Electron. J. Probab. 17: 1-19 (2012). DOI: 10.1214/EJP.v17-2002


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.


Download Citation

Alexander Gnedin. Alexander Iksanov. "Regenerative compositions in the case of slow variation: A renewal theory approach." Electron. J. Probab. 17 1 - 19, 2012.


Accepted: 17 September 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1252.60025
MathSciNet: MR2981902
Digital Object Identifier: 10.1214/EJP.v17-2002

Primary: 60F05
Secondary: 60C05 , 60K05

Keywords: First passage time , number of blocks , regenerative composition , renewal theory , weak convergence


Vol.17 • 2012
Back to Top