On the length of an external branch in the Beta-coalescent
Jean-Stéphane Dhersin,
Fabian Freund,
Arno Siri-Jégousse and
Linglong Yuan
Stochastic Processes and their Applications, 2013, vol. 123, issue 5, 1691-1715
Abstract:
In this paper, we consider Beta(2−α,α) (with 1<α<2) and related Λ-coalescents. If T(n) denotes the length of a randomly chosen external branch of the n-coalescent, we prove the convergence of nα−1T(n) when n tends to ∞, and give the limit. To this aim, we give asymptotics for the number σ(n) of collisions which occur in the n-coalescent until the end of the chosen external branch, and for the block counting process associated with the n-coalescent.
Keywords: Coalescent process; Beta-coalescent; External branch; Block counting process; Recursive construction (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)
Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414912002712
Full text for ScienceDirect subscribers only
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:123:y:2013:i:5:p:1691-1715
Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01
DOI: 10.1016/j.spa.2012.12.010
Access Statistics for this article
Stochastic Processes and their Applications is currently edited by T. Mikosch
More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().