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Asymptotic expansions for moment functionals of perturbed discrete time semi-Markov processes
Stockholm University, Faculty of Science, Department of Mathematics.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In this paper, we study mixed power-exponential moment functionals of nonlinearly perturbed semi-Markov processes in discrete time. Conditions under which the moment functionals of interest can be expanded in asymptotic power series with respect to the perturbation parameter are given. We show how the coefficients in these expansions can be computed from explicit recursive formulas. In particular, the results of the present paper have applications for studies of quasi-stationary distributions.

Keyword [en]
Semi-Markov process, Perturbation, Asymptotic expansion, Renewal equation, Solidarity property, First hitting time
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:su:diva-128972OAI: oai:DiVA.org:su-128972DiVA: diva2:918392
Available from: 2016-04-11 Created: 2016-04-11 Last updated: 2016-04-28
In thesis
1. Perturbed discrete time stochastic models
Open this publication in new window or tab >>Perturbed discrete time stochastic models
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis, nonlinearly perturbed stochastic models in discrete time are considered. We give algorithms for construction of asymptotic expansions with respect to the perturbation parameter for various quantities of interest. In particular, asymptotic expansions are given for solutions of renewal equations, quasi-stationary distributions for semi-Markov processes, and ruin probabilities for risk processes.

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Stockholm University, 2016. 48 p.
Keyword
Renewal equation, Perturbation, Asymptotic expansion, Regenerative process, Risk process, Semi-Markov process, Markov chain, Quasi-stationary distribution, Ruin probability, First hitting time, Solidarity property
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-128979 (URN)978-91-7649-422-6 (ISBN)
Public defence
2016-06-02, Sal 14, hus 5, Kräftriket, Roslagsvägen 101, Stockholm, 13:00 (English)
Opponent
Supervisors
Note

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 4: Manuscript. Paper 5: Manuscript. Paper 6: Manuscript.

Available from: 2016-05-10 Created: 2016-04-11 Last updated: 2016-04-28Bibliographically approved

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arXiv:1603.05891

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Petersson, Mikael
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