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December 2011 On Λ-coalescents with dust component
Alexander Gnedin, Alexander Iksanov, Alexander Marynych
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J. Appl. Probab. 48(4): 1133-1151 (December 2011). DOI: 10.1239/jap/1324046023

Abstract

We consider the Λ-coalescent processes with a positive frequency of singleton clusters. The class in focus covers, for instance, the beta(a, b)-coalescents with a > 1. We show that some large-sample properties of these processes can be derived by coupling the coalescent with an increasing Lévy process (subordinator), and by exploiting parallels with the theory of regenerative composition structures. In particular, we discuss the limit distributions of the absorption time and the number of collisions.

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Alexander Gnedin. Alexander Iksanov. Alexander Marynych. "On Λ-coalescents with dust component." J. Appl. Probab. 48 (4) 1133 - 1151, December 2011. https://doi.org/10.1239/jap/1324046023

Information

Published: December 2011
First available in Project Euclid: 16 December 2011

zbMATH: 1242.60077
MathSciNet: MR2896672
Digital Object Identifier: 10.1239/jap/1324046023

Subjects:
Primary: 60C05 , 60G09
Secondary: 60F05 , 60J10 , 60K05

Keywords: Absorption time , coupling , Lambda-coalescent , number of collisions , regenerative composition structure , subordinator

Rights: Copyright © 2011 Applied Probability Trust

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Vol.48 • No. 4 • December 2011
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