This presentation concerns statistical topics of semi-Markov processes, as well as new types of processes of Markov or semi-Markov type, capable of capturing some features that are important for applications. After introducing the semi-Markov framework and discussing some statistical techniques, we first present the so called drifting (semi-)Markov models. These are non-homogeneous Markov models for which the Markov transition matrix is a linear (polynomial) function/mixture of two (several) (semi-)Markov kernels. This is a “smooth” alternative to the hypothesis of homogeneity with respect to time that is used in many mathematical models. Applications in reliability/survival analysis will also be considered. Second, we will introduce and investigate step semi-Markov processes ; these are semi-Markov processes for which an additional insight is brought : the sojourn time in a state before making a transition represents the addition of two or several times that correspond to different physical causes.

This talk is mainly based on:

V. S. Barbu, N. Vergne, Reliability and survival analysis for drifting Markov models: modelling and estimation, Methodology and Computing in Applied Probability, 1-23, 2018

V. S. Barbu, G. D'Amico, R. Manca, F. Petroni, Step semi-Markov models and application to manpower management, ESAIM: Probability and Statistics, 20, 555-571, 2016