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. |
5. | Publisher | Organizing agency, location | |
6. | Contributor | Sponsor(s) | |
7. | Date | (YYYY-MM-DD) | 2011-08-09 |
8. | Type | Status & genre | Peer-reviewed Article |
8. | Type | Type | |
9. | Format | File format | |
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 | |
14. | Coverage | Geo-spatial location, chronological period, research sample (gender, age, etc.) | |
15. | Rights | Copyright and permissions | The Electronic Journal of Probability applies the Creative Commons Attribution License (CCAL) to all articles we publish in this journal. Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles published in EJP, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available. Summary of the Creative Commons Attribution License You are free
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