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August 2004 Local limit theory and large deviations for supercritical Branching processes
Peter E. Ney, Anand N. Vidyashankar
Ann. Appl. Probab. 14(3): 1135-1166 (August 2004). DOI: 10.1214/105051604000000242

Abstract

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.

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Peter E. Ney. Anand N. Vidyashankar. "Local limit theory and large deviations for supercritical Branching processes." Ann. Appl. Probab. 14 (3) 1135 - 1166, August 2004. https://doi.org/10.1214/105051604000000242

Information

Published: August 2004
First available in Project Euclid: 13 July 2004

zbMATH: 1084.60542
MathSciNet: MR2071418
Digital Object Identifier: 10.1214/105051604000000242

Subjects:
Primary: 60F10 , 60J80

Keywords: branching processes , large deviations , local limit theorems.

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.14 • No. 3 • August 2004
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