Asymptotic Behavior of Critical Primitive Multi-Type Branching Processes with Immigration
Under natural assumptions a Feller-type diffusion approximation is derived for critical multi-type branching processes with immigration when the offspring mean matrix is primitive (in other words, positively regular). Namely, it is proved that a sequence of appropriately scaled random step functions...
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| Published in | Stochastic analysis and applications Vol. 32; no. 5; pp. 727 - 741 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Taylor & Francis
03.09.2014
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| ISSN | 0736-2994 1532-9356 |
| DOI | 10.1080/07362994.2014.939542 |
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| Abstract | Under natural assumptions a Feller-type diffusion approximation is derived for critical multi-type branching processes with immigration when the offspring mean matrix is primitive (in other words, positively regular). Namely, it is proved that a sequence of appropriately scaled random step functions formed from a sequence of critical primitive multi-type branching processes with immigration converges weakly toward a squared Bessel process supported by a ray determined by the Perron vector of the offspring mean matrix. |
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| AbstractList | Under natural assumptions a Feller-type diffusion approximation is derived for critical multi-type branching processes with immigration when the offspring mean matrix is primitive (in other words, positively regular). Namely, it is proved that a sequence of appropriately scaled random step functions formed from a sequence of critical primitive multi-type branching processes with immigration converges weakly toward a squared Bessel process supported by a ray determined by the Perron vector of the offspring mean matrix. |
| Author | Ispány, Márton Pap, Gyula |
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| Cites_doi | 10.1016/j.spl.2009.04.008 10.1007/978-3-662-22132-7 10.1007/978-1-4612-1862-3_14 10.1007/978-3-642-65371-1 10.1017/CBO9780511810817 10.1007/978-1-4612-0949-2 10.1007/s10474-009-9099-5 10.1016/0304-4149(89)90092-6 10.1017/CBO9780511629136 10.1007/978-3-642-11156-3 10.2307/1427238 10.1239/jap/1143936261 10.1007/978-3-662-05265-5 10.2307/3211974 10.1214/aos/1176325509 10.1002/9780470316658 10.1016/j.spa.2010.11.005 10.1525/9780520411586-018 10.1214/aoms/1177699266 |
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| Snippet | Under natural assumptions a Feller-type diffusion approximation is derived for critical multi-type branching processes with immigration when the offspring mean... |
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| SubjectTerms | Approximation Asymptotic properties Critical primitive multi-type branching processes with immigration Diffusion Mathematical analysis Primary: 60J80 Secondary: 60J60 Squared Bessel processes Step functions Stochasticity Vectors (mathematics) |
| Title | Asymptotic Behavior of Critical Primitive Multi-Type Branching Processes with Immigration |
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