Strong convergence of a class of non-homogeneous Markov arrival processes to a Poisson process

James Ledoux (1, 2)

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

In this paper, we are concerned with a time-inhomogencous version of the Markovian arrival process. Under the assumption that the environment process is asymptotically time-homogeneous, we discuss a Poisson approximation of the counting process of arrivals when the arrivals are rare. We provide a rate of convergence for the distance in variation. Poisson-type approximation for the process resulting of a special marking procedure of the arrivals is outlined.

Mots clés: Markov additive process; compound Poisson approximation

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

James Ledoux. Strong convergence of a class of non-homogeneous Markov arrival processes to a Poisson process. Statistics and Probability Letters, 2008, 78 (4), pp.445-455. ⟨10.1016/j.spi.2007.07.018⟩. ⟨hal-00359796⟩