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Critical Multitype Branching Systems: Extinction Results


 
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1. Title Title of document Critical Multitype Branching Systems: Extinction Results
 
2. Creator Author's name, affiliation, country Peter Kevei; Centro de Investigacion en Matematicas Mexico; Mexico
 
2. Creator Author's name, affiliation, country Jose Alfredo Lopez Mimbela; Centro de Investigacion en Matematicas Mexico; Mexico
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Critical branching particle system; Extinction; Markov renewal process
 
3. Subject Subject classification MSC 60J80, MSC 60K15
 
4. Description 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.
 
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7. Date (YYYY-MM-DD) 2011-08-09
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/908
 
10. Identifier Digital Object Identifier 10.1214/EJP.v16-908
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 16
 
12. Language English=en
 
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