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Upper Deviations for Split Times of Branching Processes

Part of: Limit theorems Markov processes

Published online by Cambridge University Press:  30 January 2018

Hamed Amini  and
Marc Lelarge
Hamed Amini*
Affiliation:
École Normale Supérieure and INRIA
Marc Lelarge*
Affiliation:
École Normale Supérieure and INRIA
*
∗ Postal address: INRIA-ENS Project TREC, École Normale Supérieure, 45 rue d'Ulm, 75005 Paris, France.
∗ Postal address: INRIA-ENS Project TREC, École Normale Supérieure, 45 rue d'Ulm, 75005 Paris, France.
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Abstract

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Upper deviation results are obtained for the split time of a supercritical continuous-time Markov branching process. More precisely, we establish the existence of logarithmic limits for the likelihood that the split times of the process are greater than an identified value and determine an expression for the limiting quantity. We also give an estimation for the lower deviation probability of the split times, which shows that the scaling is completely different from the upper deviations.

Keywords

Continuous-time branching processsplit timelarge deviation

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60F10: Large deviations
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 4 , December 2012 , pp. 1134 - 1143
Copyright
© Applied Probability Trust 

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