Central limit theorem for a critical multi-type branching process in random environment
Probability
2021-10-27 v2
Abstract
Let (Z n) n0 with Z n = (Z n (i, j)) 1i,jp be a p multi-type critical branching process in random environment, and let M n be the expectation of Z n given a fixed environment. We prove theorems on convergence in distribution of sequences of branching processes Zn |Mn| /|Z n | > 0 and ln Zn \sqrt n /|Z n | > 0. These theorems extend similar results for single-type critical branching process in random environment.
Cite
@article{arxiv.2006.10994,
title = {Central limit theorem for a critical multi-type branching process in random environment},
author = {E. Le Page and M. Peigné and C. Pham},
journal= {arXiv preprint arXiv:2006.10994},
year = {2021}
}