Local limit theory and large deviations for supercritical Branching processes
概率论
2007-05-23 v1
摘要
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.
引用
@article{arxiv.math/0407059,
title = {Local limit theory and large deviations for supercritical Branching processes},
author = {Peter E. Ney and Anand N. Vidyashankar},
journal= {arXiv preprint arXiv:math/0407059},
year = {2007}
}