Geometric rho-mixing property of the interarrival times of a stationary Markovian Arrival Process

Loïc Hervé (1, 2) , James Ledoux (2, 1)

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

In this note, the sequence of the interarrivals of a stationary Markovian Arrival process is shown to be $\rho$-mixing with a geometric rate of convergence when the driving process is $\rho$-mixing. This provides an answer to an issue raised in the recent paper by P. Ramirez-Cobo and E. Carrizosa on the geometric convergence of the autocorrelation function of the stationary Markovian Arrival process.

Mots clés: Markov renewal process

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

Loïc Hervé, James Ledoux. Geometric rho-mixing property of the interarrival times of a stationary Markovian Arrival Process. Journal of Applied Probability, 2013, 50 (2), pp.598-601. ⟨hal-00838160v2⟩