Université Marne-la-Vallée,
Equipe d'Analyse et de Mathématiques Appliquées,
5 Bd Descartes, Champs-sur-Marne,
77454 Marne-la-Vallée Cedex 2, France.
CNRS, UMR 5523-LMC,
Equipe de Statistique et de Modélisation Stochastique,
BP 53, 38041 Grenoble Cedex 9, France
In this note, we investigate how various forms of stability properties for a single Markov chain over a general state space can be transferred to the m-fold product Markov chain, i.e. the Markov chain over the product state space resulting from the observation of m iid copies of the original chain. The stability properties are based on the drift criteria given in Meyn and Tweedie (1993). We show that the weakest drift conditions may not even be carried over to the product Markov chain, and that the strongest forms of drift criteria transfer properly to the product chain. We also provide minimal conditions for the product chain to be Harris recurrent, positive Harris or ergodic, and give similar results for an interacting particule system.
Preprint no 06/2000, Université Marne-la-Vallée, 12 pages.