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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Bibliographic Details
Published inStochastic analysis and applications Vol. 32; no. 5; pp. 727 - 741
Main Authors Ispány, Márton, Pap, Gyula
Format Journal Article
LanguageEnglish
Published Taylor & Francis 03.09.2014
Subjects
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)
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ISSN0736-2994
1532-9356
DOI10.1080/07362994.2014.939542

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Summary: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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ISSN:0736-2994
1532-9356
DOI:10.1080/07362994.2014.939542