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arXiv · 0710.2755

Reduced branching processes with very heavy tails

Andreas N. Lagerås·Serik Sagitov
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Abstract

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.

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Andreas N. Lagerås, Serik Sagitov. 2007-10-15. Reduced branching processes with very heavy tails. https://arxiv.org/abs/0710.2755

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