Nonlinearly Perturbed Renewal Equations: asymptotic Results and Applications
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
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.
Mälardalen University Press Dissertations, ISSN 1651-4238 ; 106
Nonlinearly perturbed renewal equation, perturbed renewal equation, nonlinear perturbation, non-polynomial perturbation, perturbed risk process, perturbed storage process
Research subject Mathematics/Applied Mathematics
IdentifiersURN: urn:nbn:se:mdh:diva-12953ISBN: 978-91-7485-032-1OAI: oai:DiVA.org:mdh-12953DiVA: diva2:438488
2011-10-28, Gamma, Högskoleplan 1, Mälardalens Högskola, Västerås, 13:15 (English)
Gyllenberg, Mats, professor
Silvestrov, Dmitrii, professorMalyarenko, Anatoliy, docent
List of papers