Strong convergence of a class of non-homogeneous Markov arrival processes to a Poisson process

James Ledoux

Statistics & Probability Letters, 2008, vol. 78, issue 4, 445-455

Abstract: In this paper, we are concerned with a time-inhomogeneous version of the Markovian arrival process. Under the assumption that the environment process is asymptotically time-homogeneous, we discuss a Poisson approximation of the counting process of arrivals when the arrivals are rare. We provide a rate of convergence for the distance in variation. Poisson-type approximation for the process resulting of a special marking procedure of the arrivals is outlined.

Keywords: Markov; additive; process; Compound; Poisson; approximation (search for similar items in EconPapers)
Date: 2008
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