Marcel F. Neuts, Ushio Sumita, Yoshitaka Takahashi, "Renewal characterization of Markov modulated Poisson processes", International Journal of Stochastic Analysis, vol. 2, Article ID 531849, 18 pages, 1989. https://doi.org/10.1155/S1048953389000043
Renewal characterization of Markov modulated Poisson processes
A Markov Modulated Poisson Process (MMPP) defined on a Markov chain is a pure jump process where jumps of occur according to a Poisson process with intensity whenever the Markov chain is in state i. is called strongly renewal if is a renewal process for an arbitrary initial probability vector of with full support on . is called weakly renewal if there exists an initial probability vector of such that the resulting MMPP is a renewal process. The purpose of this paper is to develop general characterization theorems for the class and some sufficiency theorems for the class in terms of the first passage times of the bivariate Markov chain . Relevance to the lumpability of is also studied.
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