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Geometric \(\rho \)-mixing property of the interarrival times of a stationary Markovian arrival process. (English) Zbl 1270.60075
Summary: 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 work by P. Ramírez-Cobo and E. Carrizosa [J. Appl. Probab. 49, No. 1, 295–302 (2012; Zbl 1236.60047)] on the geometric convergence of the autocorrelation function of a stationary Markovian arrival process.
MSC:
60J05 Discrete-time Markov processes on general state spaces
60K15 Markov renewal processes, semi-Markov processes
Citations:
Zbl 1236.60047
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References:
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