Recursive filters for partially observable finite Markov chains

James Ledoux (1, 2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 INSA Rennes - Institut National des Sciences Appliquées - Rennes

In this note, we consider discrete-time finite Markov chains and assume that they are only partly observed. We obtain finite-dimensional normalized filters for basic statistics associated with such processes. Recursive equations for these filters are derived by means of simple computations involving conditional expectations. An application to the estimation of parameters of the so-called discrete-time batch Markovian arrival process is outlined.

Mots clés: Time-inhomogeneous Markov chain; hidden Markov chain; D-BMAP; EM-algorithm

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

James Ledoux. Recursive filters for partially observable finite Markov chains. Journal of Applied Probability, 2005, 42 (3), pp.684-697. ⟨hal-00837502⟩