DECOMPOSITION OF A SEMI‐MARKOV PROCESS UNDER A MARKOVIAN RULE
Erhan Çınlar · Australian Journal of Statistics · 1966
Summary Consider a semi‐Markov process {X(t), t>0} with transition epochs T 0 T 1 , T 2 …. Suppose that at each one of the epochs {T n } one of R possible events, E 1 , E 2 ,…, E R can happen, where the occurrences of successive events form a Markov chain. for a fixed r, let the times the event E r happens be U o U 1 , U 2 ,…. In this paper we are interested in the process {Y(t), t>0)} where Y(t)=X(U k ) if and only if U k ≤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.