Author:
Fahady K. S.,Quine M. P.,Vere-Jones D.
Abstract
The behaviour of the Galton-Watson process in near critical conditions is discussed, both with and without immigration. Limit theorems are obtained which show that, suitably normalized, and conditional on non-extinction when there is no immigration, the number of individuals remaining in the population after a large number of generations has approximately a gamma distribution. The error estimates are uniform within a specified class of offspring distributions, and are independent of whether the critical situation is approached from above or below. These results parallel those given for continuous time branching processes by Sevast'yanov (1959), and extend recent work by Nagaev and Mohammedhanova (1966), Quineand Seneta (1969), and Seneta (1970).
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献