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The time to absorption in Λ-coalescents

Part of: Markov processes Limit theorems

Published online by Cambridge University Press:  01 February 2019

Götz Kersting  and
Anton Wakolbinger
Götz Kersting*
Affiliation:
Goethe University Frankfurt
Anton Wakolbinger*
Affiliation:
Goethe University Frankfurt
*
Institute of Mathematics, Goethe University Frankfurt, Robert Mayer Strasse 10, 60325 Frankfurt am Main, Germany. Email address: [email protected]
Institute of Mathematics, Goethe University Frankfurt, Robert Mayer Strasse 10, 60325 Frankfurt am Main, Germany. Email address: [email protected]
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Abstract

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We present a law of large numbers and a central limit theorem for the time to absorption of Λ-coalescents with dust started from n blocks, as n→∞. The proofs rely on an approximation of the logarithm of the block-counting process by means of a drifted subordinator.

Keywords

Coalescenttime to absorptionlaw of large numberscentral limit theoremsubordinator with drift

MSC classification

Primary: 60J75: Jump processes
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 60F05: Central limit and other weak theorems
Type
Original Article
Information
Advances in Applied Probability , Volume 50 , Issue A: Branching and Applied Probability , December 2018 , pp. 177 - 190
Copyright
Copyright © Applied Probability Trust 2018 

References

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