A critical branching process with immigration in random environment
Probability
2020-03-17 v1
Abstract
A Galton-Watson branching process with immigration evolving in a random environment is considered. Its associated random walk is assumed to be oscillating. We prove a functional limit theorem in which the process under consideration is normalized by a random coefficient depending on the random environment only. The distribution of the limiting process is described in terms of a strictly stable Levy process and a sequence of independent and identically distributed random variables which is independent of this process.
Cite
@article{arxiv.2003.06590,
title = {A critical branching process with immigration in random environment},
author = {V. I. Afanasyev},
journal= {arXiv preprint arXiv:2003.06590},
year = {2020}
}
Comments
34 pages, 0 figures, journal paper