Mikael Petersson: Asymptotic Expansions for Perturbed Discrete Time Renewal Equations
Time: Wed 2013-11-20 15.15
Location: The Cramér room (room 306), building 6, Kräftriket, Department of mathematics, Stockholm university
Subject area: Mathematical statistics
Doctoral student: Mikael Petersson
Opponent: Henrik Hult, KTH
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.