Perturbed discrete time stochastic models

Detta är en avhandling från Stockholm : Department of Mathematics, Stockholm University

Författare: Mikael Petersson; Stockholms Universitet.; [2016]

Nyckelord: NATURVETENSKAP; NATURAL SCIENCES; Renewal equation; Perturbation; Asymptotic expansion; Regenerative process; Risk process; Semi-Markov process; Markov chain; Quasi-stationary distribution; Ruin probability; First hitting time; Solidarity property; matematisk statistik; Mathematical Statistics;

Sammanfattning: In this thesis, nonlinearly perturbed stochastic models in discrete time are considered. We give algorithms for construction of asymptotic expansions with respect to the perturbation parameter for various quantities of interest. In particular, asymptotic expansions are given for solutions of renewal equations, quasi-stationary distributions for semi-Markov processes, and ruin probabilities for risk processes.

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