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A Note on the Dependence Structure of the Two-State Markovian Arrival Process

Part of: Markov processes Stochastic processes

Published online by Cambridge University Press:  04 February 2016

Pepa Ramírez-Cobo  and
Emilio Carrizosa
Pepa Ramírez-Cobo*
Affiliation:
University of Seville
Emilio Carrizosa*
Affiliation:
University of Seville
*
∗ Postal address: Institute of Mathematics, University of Seville, Avda. Reina Mercedes s/n, 41012 Seville, Spain. Email address: [email protected]
∗∗ Postal address: Department of Statistics and Operations Research, University of Seville, Avda. Reina Mercedes s/n, 41012 Seville, Spain. Email address: [email protected]
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Abstract

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The Markovian arrival process generalizes the Poisson process by allowing for dependent and nonexponential interarrival times. We study the autocorrelation function of the two-state Markovian arrival process. Our findings show that the correlation structure of such a process has a very specific pattern, namely, it always converges geometrically to zero. Moreover, the signs of the autocorrelation coefficients are either constant or alternating.

Keywords

Markovian arrival processMarkov renewal processautocorrelation function

MSC classification

Primary: 60G55: Point processes
Secondary: 60J05: Discrete-time Markov processes on general state spaces
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 1 , March 2012 , pp. 295 - 302
Copyright
© Applied Probability Trust 

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