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Quasi-Stationary Asymptotics for Perturbed Semi-Markov Processes in Discrete Time
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 12017 (English)In: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 19, no 4, p. 1047-1074Article in journal (Refereed) Published
Abstract [en]

We consider a discrete time semi-Markov process where the characteristics defining the process depend on a small perturbation parameter. It is assumed that the state space consists of one finite communicating class of states and, in addition, one absorbing state. Our main object of interest is the asymptotic behavior of the joint probabilities of the position of the semi-Markov process and the event of non-absorption as time tends to infinity and the perturbation parameter tends to zero. The main result gives exponential expansions of these probabilities together with a recursive algorithm for computing the coefficients in the expansions. An application to perturbed epidemic SIS models is discussed.

Place, publisher, year, edition, pages
2017. Vol. 19, no 4, p. 1047-1074
Keywords [en]
Semi-Markov process, Perturbation, Asymptotic expansion, Regenerative process, Renewal equation, Solidarity property, First hitting time
National Category
Mathematics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:su:diva-148811DOI: 10.1007/s11009-016-9530-7ISI: 000413792200004OAI: oai:DiVA.org:su-148811DiVA, id: diva2:1156812
Conference
15th Applied Stochastic Models and Data Analysis International Conference (ASMDA), Piraeus, Greece June 30-July 04, 2015
Available from: 2017-11-14 Created: 2017-11-14 Last updated: 2017-11-14Bibliographically approved
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. p. 48
Keywords
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: 2017-11-14Bibliographically approved

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