Some distribution and moment formulae for the Markov renewal process
Published online by Cambridge University Press: 24 October 2008
Extract
1. Introduction. A Markov Renewal Process (MRP) with m(<∞) states is one which records at each time t, the number of times a system visits each of the m states up to time t, if the system moves from state to state according to a Markov chain with transition probability matrix P0 = [pij] and if the time required for each successive move is a random variable whose distribution function (d.f.) depends on the two states between which the move is made. Thus, if the system moves from state i to state j, the holding time in the state i has Fij(x) as its d.f. (i, j = 1,2, …, m).
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 1 , July 1970 , pp. 159 - 166
- Copyright
- Copyright © Cambridge Philosophical Society 1970
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