Abstract: | Consider a semi-Markov process {X(t), t>0} with transition epochs T0 T1, T2…. Suppose that at each one of the epochs {Tn} one of R possible events, E1, E2,…, ER can happen, where the occurrences of successive events form a Markov chain. for a fixed r, let the times the event Er happens be Uo U1, 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. |