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Analytical and Numerical Studies of Perturbed Renewal Equations with Multivariate Non-Polynomial Perturbations
Mälardalen University, School of Education, Culture and Communication.ORCID iD: 0000-0002-0835-7536
2010 (English)In: Journal of Applied Quantitative Methods, ISSN 1842-4562, Vol. 5, no 3, 411-428 p.Article in journal (Refereed) Published
Abstract [en]

The object of study is a model of nonlinearly perturbed continuous-time renewal equation with multivariate non-polynomial perturbations. The characteristics of the distribution generating the renewal equation are assumed to have expansions in a perturbation parameter with respect to a non-polynomial asymptotic. Exponential asymptotics for such a model as well as their applications are given. Numerical studies are performed to gain insights into the asymptotical results.

Place, publisher, year, edition, pages
Association for Development through Science and Education, Romania (ADSE). , 2010. Vol. 5, no 3, 411-428 p.
Keyword [en]
perturbed renewal equation, nonlinear perturbation, non-polynomial perturbation, perturbed risk process, ruin probability
National Category
Computational Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-11698OAI: oai:DiVA.org:mdh-11698DiVA: diva2:394322
Available from: 2011-02-02 Created: 2011-02-02 Last updated: 2015-06-29Bibliographically approved
In thesis
1. Nonlinearly Perturbed Renewal Equations: asymptotic Results and Applications
Open this publication in new window or tab >>Nonlinearly Perturbed Renewal Equations: asymptotic Results and Applications
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis we investigate a model of nonlinearly perturbed continuous-time renewal equation. Some characteristics of the renewal equation are assumed to have non-polynomial perturbations, more specifically they can be expanded with respect to a non-polynomial asymptotic scale. The main result of the present study is exponential asymptotic expansions for the solution of the perturbed renewal equation. These asymptotic results are also applied to various applied probability models like perturbed risk processes, perturbed M/G/1 queues and perturbed dam/storage processes.

The thesis is based on five papers where the model described above is successively studied.

Place, publisher, year, edition, pages
Västerås: Mälardalen University, 2011. 33 p.
Series
Mälardalen University Press Dissertations, ISSN 1651-4238 ; 106
Keyword
Nonlinearly perturbed renewal equation, perturbed renewal equation, nonlinear perturbation, non-polynomial perturbation, perturbed risk process, perturbed storage process
National Category
Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-12953 (URN)978-91-7485-032-1 (ISBN)
Public defence
2011-10-28, Gamma, Högskoleplan 1, Mälardalens Högskola, Västerås, 13:15 (English)
Opponent
Supervisors
Available from: 2011-09-05 Created: 2011-09-02 Last updated: 2015-06-29Bibliographically approved

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