Some algebraic methods in semi-Markov processes

Vlad Stefan Barbu , Nikolaos Limnios (1)

1 LMAC - Laboratoire de Mathématiques Appliquées de Compiègne

This article is concerned with algebraic methods develoed for discrete-time semi-Markov processes with state space. after a short presentation of infinite matrices and associated operations, we discribe the discrete-time semi-Markov setting. Then, we present some elements of Markov renewal theory and we obtain the mean hitting time of a subset of the state space for this type of process. A specilization of these results to the finite state space cas is also presented. We end with several concluding remarks.

Mots clés: Semi-Markov chains; Countable state space; Algebraic methods; Markov renewal theory; Reliability; Hitting times

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Vlad Stefan Barbu, Nikolaos Limnios. Some algebraic methods in semi-Markov processes. Algebraic Methods in Statistics and Probability, vol. 2, American Mathematical Society, pp.19-35, 2010, Contemporary Mathematics, vol. 516, ⟨10.1090/conm/516/10163⟩. ⟨hal-00530333⟩