References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt145",{id:"formSmash:upper:j_idt145",widgetVar:"widget_formSmash_upper_j_idt145",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt146_j_idt148",{id:"formSmash:upper:j_idt146:j_idt148",widgetVar:"widget_formSmash_upper_j_idt146_j_idt148",target:"formSmash:upper:j_idt146:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Perturbed discrete time stochastic modelsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2016 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Stockholm: Department of Mathematics, Stockholm University , 2016. , 48 p.
##### Keyword [en]

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: urn:nbn:se:su:diva-128979ISBN: 978-91-7649-422-6OAI: oai:DiVA.org:su-128979DiVA: diva2:918673
##### Public defence

2016-06-02, Sal 14, hus 5, Kräftriket, Roslagsvägen 101, Stockholm, 13:00 (English)
##### Opponent

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##### Supervisors

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#####

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##### Note

##### List of papers

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.

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 approved1. Exponential Expansions for Perturbed Discrete Time Renewal Equations$(function(){PrimeFaces.cw("OverlayPanel","overlay660252",{id:"formSmash:j_idt423:0:j_idt427",widgetVar:"overlay660252",target:"formSmash:j_idt423:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Quasi-Stationary Distributions for Perturbed Discrete Time Regenerative Processes$(function(){PrimeFaces.cw("OverlayPanel","overlay660265",{id:"formSmash:j_idt423:1:j_idt427",widgetVar:"overlay660265",target:"formSmash:j_idt423:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Asymptotics of Ruin Probabilities for Perturbed Discrete Time Risk Processes$(function(){PrimeFaces.cw("OverlayPanel","overlay660274",{id:"formSmash:j_idt423:2:j_idt427",widgetVar:"overlay660274",target:"formSmash:j_idt423:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. Quasi-stationary asymptotics for perturbed semi-Markov processes in discrete time$(function(){PrimeFaces.cw("OverlayPanel","overlay918380",{id:"formSmash:j_idt423:3:j_idt427",widgetVar:"overlay918380",target:"formSmash:j_idt423:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

5. Asymptotic expansions for moment functionals of perturbed discrete time semi-Markov processes$(function(){PrimeFaces.cw("OverlayPanel","overlay918392",{id:"formSmash:j_idt423:4:j_idt427",widgetVar:"overlay918392",target:"formSmash:j_idt423:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

6. Asymptotics for quasi-stationary distributions of perturbed discrete time semi-Markov processes$(function(){PrimeFaces.cw("OverlayPanel","overlay918397",{id:"formSmash:j_idt423:5:j_idt427",widgetVar:"overlay918397",target:"formSmash:j_idt423:5:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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