Journal of Applied Probability

Upper deviations for split times of branching processes

Hamed Amini and Marc Lelarge

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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.

Article information

J. Appl. Probab., Volume 49, Number 4 (2012), 1134-1143.

First available in Project Euclid: 5 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60F10: Large deviations

Continuous-time branching process split time large deviation


Amini, Hamed; Lelarge, Marc. Upper deviations for split times of branching processes. J. Appl. Probab. 49 (2012), no. 4, 1134--1143. doi:10.1239/jap/1354716662.

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