DECOMPOSITION OF A SEMI‐MARKOV PROCESS UNDER A MARKOVIAN RULE
- 1 November 1966
- journal article
- Published by Wiley in Australian Journal of Statistics
- Vol. 8 (3) , 163-170
- https://doi.org/10.1111/j.1467-842x.1966.tb00266.x
Abstract
Summary: Consider a semi‐Markov process {X(t), t>0} with transition epochs T0T1, T2…. Suppose that at each one of the epochs {Tn} one of R possible events, E1, E2,…, ERcan happen, where the occurrences of successive events form a Markov chain. for a fixed r, let the times the event Erhappens be UoU1, U2,…. In this paper we are interested in the process {Y(t), t>0)} where Y(t)=X(Uk) if and only if Uk≤tk+1. It will be shown that {Y(t)} is a semi‐Markov process, and its properties with respect to those of {X(t)} will be examined.Keywords
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