Marked point processes as limits of Markovian arrival streams
Journal of Applied Probability1993Vol. 30(2), pp. 365–372
Citations Over TimeTop 10% of 1993 papers
Abstract
A Markovian arrival stream is a marked point process generated by the state transitions of a given Markovian environmental process and Poisson arrival rates depending on the environment. It is shown that to a given marked point process there is a sequence of such Markovian arrival streams with the property that as m →∞. Various related corollaries (involving stationarity, convergence of moments and ergodicity) and counterexamples are discussed as well.
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