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Asymptotically Improper Perturbed Renewal Equations: Asymptotic Results and Their Applications
Mälardalen University, School of Education, Culture and Communication. (Matematik/tillämpad matematik, Analytical Finance)ORCID iD: 0000-0002-0835-7536
2011 (English)Report (Other academic)
Abstract [en]

We consider a family of asymptotically improper perturbed renewal equations where the characteristics of the distribution functions generating the perturbed renewal equations are perturbed in a particular way. More specifically, those characteristics are nonlinear functions of the perturbation parameter such that they can be expanded into asymptotic expansions of a non-polynomial type with respect to the perturbation parameter. We give asymptotic results, namely the exponential asymptotic expansions, for the solutions of the perturbed renewal equations. An application to perturbed storage processes is also presented.

Place, publisher, year, edition, pages
Västerås: Mälardalens University , 2011. , 21 p.
Series
School of Education, Culture and Communication, Division of Applied Mathematics, ISSN 1404-4978 ; 2011-1
Keyword [en]
Perturbed renewal equations, nonlinear perturbations, non-polynomial perturbations, perturbed storage processes
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-12917OAI: oai:DiVA.org:mdh-12917DiVA: diva2:436954
Available from: 2011-08-25 Created: 2011-08-25 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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Citation style
  • apa
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