Local limit theory and large deviations for supercritical Branching processes

2004/07/05 by Peter E. Ney, Anand N. Vidyashankar · 2 citations
Mathematics · Physics and Astronomy · #Nonlinear Partial Differential Equations #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60F10. #msc:60J80

paper · pdf · doi:10.1214/105051604000000242

published as Annals of Applied Probability 2004, Vol. 14, No. 3, 1135-1166

arxiv created 2004/07/05 · openalex publication_date 2004/07/13 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper we study several aspects of the growth of a supercritical Galton–Watson process Zn:n≥1, 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:n≥1, where Yn satisfies an LDP, particularly of Zn−1Zn+1:n≥1 conditioned on Zn≥vn.

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