The Annals of Applied Probability

Local limit theory and large deviations for supercritical Branching processes

Peter E. Ney and Anand N. Vidyashankar

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In this paper we study several aspects of the growth of a supercritical Galton–Watson process {Zn:n1}, and bring out some criticality phenomena determined by the Schröder constant. We develop the local limit theory of Zn, that is, the behavior of P(Zn=vn) as vn, and use this to study conditional large deviations of {YZn:n1}, where Yn satisfies an LDP, particularly of {Zn1Zn+1:n1} conditioned on Znvn.

Article information

Ann. Appl. Probab., Volume 14, Number 3 (2004), 1135-1166.

First available in Project Euclid: 13 July 2004

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Zentralblatt MATH identifier

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

Branching processes large deviations local limit theorems.


Ney, Peter E.; Vidyashankar, Anand N. Local limit theory and large deviations for supercritical Branching processes. Ann. Appl. Probab. 14 (2004), no. 3, 1135--1166. doi:10.1214/105051604000000242.

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