@article{EJP908,
author = {Peter Kevei and Jose Lopez Mimbela},
title = {Critical Multitype Branching Systems: Extinction Results},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {16},
year = {2011},
keywords = {Critical branching particle system; Extinction; Markov renewal process},
abstract = {We consider a critical branching particle system in $\mathbb{R}^d$, composed of individuals of a finite number of types $i\in\{1,\ldots,K\}$. Each individual of type i moves independently according to a symmetric $\alpha_i$-stable motion. We assume that the particle lifetimes and offspring distributions are type-dependent. Under the usual independence assumptions in branching systems, we prove extinction theorems in the following cases: (1) all the particle lifetimes have finite mean, or (2) there is a type whose lifetime distribution has heavy tail, and the other lifetimes have finite mean. We get a more complex dynamics by assuming in case (2) that the most mobile particle type corresponds to a finite-mean lifetime: in this case, local extinction of the population is determined by an interaction of the parameters (offspring variability, mobility, longevity) of the long-living type and those of the most mobile type. The proofs are based on a precise analysis of the occupation times of a related Markov renewal process, which is of independent interest.},
pages = {no. 50, 1356-1380},
issn = {1083-6489},
doi = {10.1214/EJP.v16-908},
url = {http://ejp.ejpecp.org/article/view/908}}