Functional limit theorems for Galton-Watson processes with very active immigration
Probability
2016-12-07 v1
Abstract
We prove weak convergence on the Skorokhod space of Galton-Watson processes with immigration, properly normalized, under the assumption that the tail of the immigration distribution has a logarithmic decay. The limits are extremal shot noise processes. By considering marginal distributions, we recover the results of Pakes [Adv. Appl. Probab., 11(1979), 31--62].
Cite
@article{arxiv.1612.01573,
title = {Functional limit theorems for Galton-Watson processes with very active immigration},
author = {Alexander Iksanov and Zakhar Kabluchko},
journal= {arXiv preprint arXiv:1612.01573},
year = {2016}
}
Comments
15 pages, 1 figure