Asymptotic Expansions for Perturbed Discrete Time Renewal Equations

Author: Mikael Petersson; Dmitrii Silvestrov; Ola Hössjer; Henrik Hult; Stockholms Universitet; []

Keywords: NATURAL SCIENCES; NATURVETENSKAP; NATURVETENSKAP; NATURAL SCIENCES; Renewal equation; Perturbation; Asymptotic expansion; Regenerative process; Quasi-stationary distribution; Risk process; Ruin probability;

Abstract: In this thesis we study the asymptotic behaviour of the solution of a discrete time renewal equation depending on a small perturbation parameter. In particular, we construct asymptotic expansions for the solution of the renewal equation and related quantities. The results are applied to studies of quasi-stationary phenomena for regenerative processes and asymptotics of ruin probabilities for a discrete time analogue of the Cramér-Lundberg risk model.

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