Reduced branching processes with very heavy tails
2008 (English)In: Journal of Applied Probability, ISSN 0021-9002, Vol. 45, no 1, 190-200 p.Article in journal (Refereed) Published
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∈(0,1]. We turn to the case of very heavy tailed reproduction distribution α=0 assuming Zubkov’s regularitycondition with parameter β∈(0,∞). Our main result gives a new asymptotic pattern for the reduced branching process conditioned on non-extinction during a long time interval.
Place, publisher, year, edition, pages
2008. Vol. 45, no 1, 190-200 p.
IdentifiersURN: urn:nbn:se:su:diva-16309OAI: oai:DiVA.org:su-16309DiVA: diva2:182829