Journal of Applied Probability

Upper deviations for split times of branching processes

Hamed Amini and Marc Lelarge

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Abstract

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

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

Dates
First available in Project Euclid: 5 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.jap/1354716662

Digital Object Identifier
doi:10.1239/jap/1354716662

Mathematical Reviews number (MathSciNet)
MR3058993

Zentralblatt MATH identifier
1275.60065

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

Keywords
Continuous-time branching process split time large deviation

Citation

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. https://projecteuclid.org/euclid.jap/1354716662


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References

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