Title: Survival analysis for semi-Markov processes
Authors: Vlad Barbu - Universite de Rouen (France) [presenting]
Abstract: Semi-Markov processes and Markov renewal processes represent a class of stochastic processes that generalize Markov and renewal processes. As it is well known, for a discrete-time (respectively continuous-time) Markov process, the sojourn time in each state is geometrically (respectively exponentially) distributed. In the semi-Markov case, the sojourn time distribution can be any distribution on N (respectively on R). This is the reason why the semi-Markov approach is much more suitable for applications than the Markov one. The purpose is to investigate some survival analysis and reliability problems for semi-Markov processes and to address some statistical topics. We start by briefly introducing the discrete-time semi-Markov framework, giving some basic definitions and results. These results are applied in order to obtain closed forms for some survival or reliability indicators, like survival/reliability function, availability, mean hitting times, etc. The nonparametric estimation of the characteristics of a semi-Markov system and of the associated survival/reliability indicators is considered. A particular attention is given to censored data in semi-Markov framework.