Strong convergence of a class of non-homogeneous Markov arrival processes to a Poisson process
Résumé
In this paper, we are concerned with a time-inhomogencous 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.
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