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Limit theorems for pure death processes coming down from infinity

Part of: Markov processes Limit theorems

Published online by Cambridge University Press:  15 September 2017

Serik Sagitov  and
Thibaut France
Serik Sagitov*
Affiliation:
Chalmers University of Technology and University of Gothenburg
Thibaut France*
Affiliation:
École Polytechnique
*
* Postal address: Mathematical Sciences, Chalmers University, Gothenburg, 412 96, Sweden. Email address: [email protected]
** Postal address: École Polytechnique, route de Saclay, 91128 Palaiseau Cedex, France.
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Abstract

In this paper we treat a pure death process coming down from infinity as a natural generalization of the death process associated with the Kingman coalescent. We establish a number of limit theorems including a strong law of large numbers and a large deviation theorem.

Keywords

Almost sure convergencelarge deviationKingman's coalescent

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60F10: Large deviations 60F15: Strong theorems
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 3 , September 2017 , pp. 720 - 731
Copyright
Copyright © Applied Probability Trust 2017 

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References

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