Asymptotic analysis of some non-homogeneous semi-Markov processes
Semi-Markov models turn out to be inadequate in some applications, see for instance (Janssen, Volpe, 1986), because the independence of the transition lengths given all the states visited, is too restrictive an assumption to be practical. In 1972, A. Iosifescu-Manu pointed out the convenience of allowing the sojourn in a state between two transitions to depend on the time when that sojourn began. She adapted the Markov renewal equation to these circumstances. A more general situation arises when the dependence is also on the number of the transitions preceding that sojourn. The foundations for the resulting non-homogeneous semi-Markov theory are in (De Dominicis, Janssen, 1984), but asymptotic theorems are still missing.
KeywordsAsymptotic Analysis Transition Kernel Finite State Space Regular Chain Markov Renewal Process
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