Reduced branching processes with very heavy tails

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The reduced Markov branching process is a stochastic model for the genealogy of an unstructured biological population. Its limit behavior in the critical case is well studied for the Zolotarev-Slack regularity parameter $α\in(0,1]$. We turn to the case of very heavy tailed reproduction distribution $α=0$ assuming Zubkov's regularity condition with parameter $β\in(0,\infty)$. Our main result gives a new asymptotic pattern for the reduced branching process conditioned on non-extinction during a long time interval.
15 pages, 1 figure

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Probability, 60J80; 60F05

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http://salesiana.dossiersoluciones.com/handle/123456789/140033

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0710.2755
 http://arxiv.org/abs/0710.2755

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arXiv