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Geometric ρ-Mixing Property of the Interarrival Times of a Stationary Markovian Arrival Process

Part of: Special processes Markov processes

Published online by Cambridge University Press:  30 January 2018

Loïc Hervé  and
James Ledoux
Loïc Hervé*
Affiliation:
INSA de Rennes, IRMAR CNRS UMR 6625
James Ledoux*
Affiliation:
INSA de Rennes, IRMAR CNRS UMR 6625
*
∗ Postal address: INSA, 20 avenue des Buttes de Coesmes, CS 70 839, 35708 Rennes cedex 7, France.
∗ Postal address: INSA, 20 avenue des Buttes de Coesmes, CS 70 839, 35708 Rennes cedex 7, France.
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Abstract

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In this note, the sequence of the interarrivals of a stationary Markovian arrival process is shown to be ρ-mixing with a geometric rate of convergence when the driving process is ρ-mixing. This provides an answer to an issue raised in the recent work of Ramirez-Cobo and Carrizosa (2012) on the geometric convergence of the autocorrelation function of the stationary Markovian arrival process.

Keywords

Markov renewal process

MSC classification

Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 60K15: Markov renewal processes, semi-Markov processes
Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 2 , June 2013 , pp. 598 - 601
Copyright
© Applied Probability Trust 

References

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