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Local limit theory and large deviations for supercritical Branching processes

Peter E. Ney·Anand N. Vidyashankar
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Abstract

In this paper we study several aspects of the growth of a supercritical Galton-Watson process {Z_n:n\ge1}, and bring out some criticality phenomena determined by the Schroder constant. We develop the local limit theory of Z_n, that is, the behavior of P(Z_n=v_n) as v_n\nearrow \infty, and use this to study conditional large deviations of {Y_{Z_n}:n\ge1}, where Y_n satisfies an LDP, particularly of {Z_n^{-1}Z_{n+1}:n\ge1} conditioned on Z_n\ge v_n.

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Peter E. Ney, Anand N. Vidyashankar. 2004-07-05. Local limit theory and large deviations for supercritical Branching processes. https://doi.org/10.1214/105051604000000242

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