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NONLINEARLY PERTURBED RENEWAL EQUATIONS: THE NON-POLYNOMIAL CASE
Mälardalen University, School of Education, Culture and Communication. (Matematik/tillämpad matematik, Analytical Finance)ORCID iD: 0000-0002-0835-7536
2012 (English)In: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, Vol. 84, p. 117-129Article in journal (Refereed) Published
Abstract [en]

Models of nonlinearly perturbed renewal equations with non-polynomial perturbations are studied. Exponential asymptotic expansions are given for the solutions to the perturbed renewal equations under consideration. An application to perturbed M/G/1/ queues is presented.

Place, publisher, year, edition, pages
Kiev, Ukraine: Kiev University (English translation by American Mathematical Society) , 2012. Vol. 84, p. 117-129
Keywords [en]
Perturbed renewal equation, non-polynomial perturbation
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-12913DOI: 10.1090/S0094-9000-2012-00865-XScopus ID: 2-s2.0-84865087490OAI: oai:DiVA.org:mdh-12913DiVA, id: diva2:436933
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. p. 33
Series
Mälardalen University Press Dissertations, ISSN 1651-4238 ; 106
Keywords
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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Ni, Ying

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