Change search
ReferencesLink to record
Permanent link

Direct link
Asymptotics for quasi-stationary distributions 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 quasi-stationary distributions of nonlinearly perturbed semi-Markov processes in discrete time. This type of distributions is of interest for the analysis of stochastic systems which have finite lifetimes, but are expected to persist for a long time. We obtain asymptotic power series expansions for quasi-stationary distributions and it is shown how the coefficients in these expansions can be computed from a recursive algorithm. As an illustration of this algorithm, we present a numerical example for a discrete time Markov chain.

Keyword [en]
Semi-Markov process, Perturbation, Quasi-stationary distribution, Asymptotic expansion, Renewal equation, Markov chain
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:su:diva-128976OAI: oai:DiVA.org:su-128976DiVA: diva2:918397
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

Open Access in DiVA

No full text

Other links

arXiv:1603.05895

Search in DiVA

By author/editor
Petersson, Mikael
By organisation
Department of Mathematics
Probability Theory and Statistics

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 3 hits
ReferencesLink to record
Permanent link

Direct link