Journal of Applied Probability

Geometric ρ-mixing property of the interarrival times of a stationary Markovian arrival process

Loïc Hervé and James Ledoux

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Abstract

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.

Article information

Source
J. Appl. Probab., Volume 50, Number 2 (2013), 598-601.

Dates
First available in Project Euclid: 19 June 2013

Permanent link to this document
https://projecteuclid.org/euclid.jap/1371648964

Digital Object Identifier
doi:10.1239/jap/1371648964

Mathematical Reviews number (MathSciNet)
MR3102503

Zentralblatt MATH identifier
1270.60075

Subjects
Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 60K15: Markov renewal processes, semi-Markov processes

Keywords
Markov renewal process

Citation

Hervé, Loïc; Ledoux, James. Geometric ρ-mixing property of the interarrival times of a stationary Markovian arrival process. J. Appl. Probab. 50 (2013), no. 2, 598--601. doi:10.1239/jap/1371648964. https://projecteuclid.org/euclid.jap/1371648964


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References

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