Todorovic, P. - In: Stochastic Processes and their Applications 45 (1993) 1, pp. 127-140
Let {Xn}[infinity]0(X0X1...) be a homogeneous Markov chain and {Tn}[infinity]0 a sequence of non-negative integer-valued r.v.'s conditionally independent given {Xn}[infinity]0. Under certain conditions {(Xn,Tn)}[infinity]0 is a Markov renewal process. The semi-Markov process {[xi]n}[infinity]0...