Marked Point Processes as Limits of Markovian Arrival Streams

摘要

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 N there is a sequence in braces: (N(sup m)) of such Markovian arrival streams with the property that N(sup m)(->(sup D))N as m -> infinity. Various related corollaries (involving stationarity, convergence of moments and ergodicity) and counterexamples are discussed as well.