Nonlinearly Perturbed Renewal Equations : asymptotic Results and Applications

Författare: Ying Ni; Dmitrii Silvestrov; Anatoliy Malyarenko; Mats Gyllenberg; Mälardalens Högskola; []

Nyckelord: NATURAL SCIENCES; NATURVETENSKAP; Nonlinearly perturbed renewal equation; perturbed renewal equation; nonlinear perturbation; non-polynomial perturbation; perturbed risk process; perturbed storage process; Mathematical statistics; Matematisk statistik; Mathematics Applied Mathematics; matematik tillämpad matematik;

Sammanfattning: 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.

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