Critical Galton-Watson branching processes with countably infinitely many types and infinite second moments
Probability
2020-03-02 v1
Abstract
We consider an indecomposable Galton-Watson branching process with countably infinitely many types. Assuming that the process is critical and allowing for infinite variance of the offspring sizes of some (or all) types of particles we describe the asymptotic behavior of the survival probability of the process and establish a Yaglom-type conditional limit theorem for the infinite-dimensional vector of the number of particles of all types.
Keywords
Cite
@article{arxiv.2002.12627,
title = {Critical Galton-Watson branching processes with countably infinitely many types and infinite second moments},
author = {V. A. Topchii and V. A. Vatutin and E. E. Dyakonova},
journal= {arXiv preprint arXiv:2002.12627},
year = {2020}
}
Comments
30 pages