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Self-normalized large deviation for supercritical branching processes

Part of: Markov processes Limit theorems

Published online by Cambridge University Press:  26 July 2018

Weijuan Chu
Weijuan Chu*
Affiliation:
Hohai University
*
* Postal address: College of Science, Hohai University, No. 8 Focheng Road West, Nanjing, Jiangsu Province, 210098, P. R. China. Email address: chuwj@hhu.edu.cn
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Abstract

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We consider a supercritical branching process (Zn, n ≥ 0) with offspring distribution (pk, k ≥ 0) satisfying p0 = 0 and p1 > 0. By applying the self-normalized large deviation of Shao (1997) for independent and identically distributed random variables, we obtain the self-normalized large deviation for supercritical branching processes, which is the self-normalized version of the result obtained by Athreya (1994). The self-normalized large deviation can also be generalized to supercritical multitype branching processes.

Keywords

Self-normalized large deviationsupercritical branching processmultitype branching process

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60F10: Large deviations
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 2 , June 2018 , pp. 450 - 458
Copyright
Copyright © Applied Probability Trust 2018 

References

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