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Markov Chains, Renewal, Branching and Coalescent Processes: Four Topics in Probability Theory
Stockholm University, Faculty of Science, Department of Mathematics.
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: urn:nbn:se:su:diva-6637ISBN: 91-7155-375-4 (print)OAI: oai:DiVA.org:su-6637DiVA: diva2:196791
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
List of papers
1. Central limit theorems for contractive Markov chains
Open this publication in new window or tab >>Central limit theorems for contractive Markov chains
2005 In: Nonlinearity, ISSN 0951-7715, Vol. 18, no 5, 1955-1965 p.Article in journal (Refereed) Published
Identifiers
urn:nbn:se:su:diva-24114 (URN)
Note
Part of urn:nbn:se:su:diva-6637Available from: 2007-02-14 Created: 2007-02-13Bibliographically approved
2. A renewal-process-type expression for the moments of inverse subordinators
Open this publication in new window or tab >>A renewal-process-type expression for the moments of inverse subordinators
2005 In: Journal of Applied Probability, ISSN 0021-9002, Vol. 42, no 4, 1134-1144 p.Article in journal (Refereed) Published
Identifiers
urn:nbn:se:su:diva-24115 (URN)
Note
Part of urn:nbn:se:su:diva-6637Available from: 2007-02-14 Created: 2007-02-13Bibliographically approved
3. Genealogy for supercritical branching processes
Open this publication in new window or tab >>Genealogy for supercritical branching processes
2006 In: Journal of Applied Probability, ISSN 0021-9002, Vol. 43, no 4, 1066-1076 p.Article in journal (Refereed) Published
Identifiers
urn:nbn:se:su:diva-24116 (URN)
Note
Part of urn:nbn:se:su:diva-6637Available from: 2007-02-14 Created: 2007-02-13Bibliographically approved
4. A population model for Lambda-coalescents with neutral mutations
Open this publication in new window or tab >>A population model for Lambda-coalescents with neutral mutations
2007 In: Electronic Communications in Probability, ISSN 1083-589X, Vol. 12, 9-20 p.Article in journal (Refereed) Published
Identifiers
urn:nbn:se:su:diva-24117 (URN)000244078100001 ()
Note
Part of urn:nbn:se:su:diva-6637Available from: 2007-02-14 Created: 2007-02-13Bibliographically approved

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