On weak lumpability of denumerable Markov chains

James Ledoux (1, 2)

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

We consider weak lumpability of denumerable Markov chains evolving in discrete or continuous time. Specifically, we study the properties of the set of all initial distributions of the starting chain leading to an aggregated homogeneous Markov chain with respect to a partition of the state space.

Mots clés: Weak Lumpability; Positive recurrence; $R$-positivity; Quasi-stationary distribution; Uniform semi-group

Domaines: Probabilités [math.PR]

James Ledoux. On weak lumpability of denumerable Markov chains. Statistics and Probability Letters, 1995, 25, pp.329-339. ⟨hal-00852300⟩