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Genealogy for supercritical branching processes
Stockholm University, Faculty of Science, Department of Mathematics.
2006 In: Journal of Applied Probability, ISSN 0021-9002, Vol. 43, no 4, 1066-1076 p.Article in journal (Refereed) Published
Place, publisher, year, edition, pages
2006. Vol. 43, no 4, 1066-1076 p.
Identifiers
URN: urn:nbn:se:su:diva-24116OAI: oai:DiVA.org:su-24116DiVA: diva2:196789
Note
Part of urn:nbn:se:su:diva-6637Available from: 2007-02-14 Created: 2007-02-13Bibliographically approved
In thesis
1. Markov Chains, Renewal, Branching and Coalescent Processes: Four Topics in Probability Theory
Open this publication in new window or tab >>Markov Chains, Renewal, Branching and Coalescent Processes: Four Topics in Probability Theory
2007 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of four papers.

In paper 1, we prove central limit theorems for Markov chains under (local) contraction conditions. As a corollary we obtain a central limit theorem for Markov chains associated with iterated function systems with contractive maps and place-dependent Dini-continuous probabilities.

In paper 2, properties of inverse subordinators are investigated, in particular similarities with renewal processes. The main tool is a theorem on processes that are both renewal and Cox processes.

In paper 3, distributional properties of supercritical and especially immortal branching processes are derived. The marginal distributions of immortal branching processes are found to be compound geometric.

In paper 4, a description of a dynamic population model is presented, such that samples from the population have genealogies as given by a Lambda-coalescent with mutations. Depending on whether the sample is grouped according to litters or families, the sampling distribution is either regenerative or non-regenerative.

Place, publisher, year, edition, pages
Stockholm: Matematiska institutionen, 2007. 80 p.
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-6637 (URN)91-7155-375-4 (ISBN)
Public defence
2007-03-14, sal 14, hus 5, Kräftriket, Stockholm, 13:00
Opponent
Supervisors
Available from: 2007-02-14 Created: 2007-02-13Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • ieee
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  • Other style
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  • de-DE
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