The number of visits to a subset of the state space by a discrete- parameter semi-Markov process
A discrete-parameter irreducible semi-Markov process with a finite state space is considered. The state space is the union of two disjoint nonempty subsets \(A_1\) and \(A_2\). The distribution of a random number of transitions \(A_1 \to A_2\) during the first \(t + 1\) time instants \((t \geq 1)\) is investigated. A compact formula for this distribution in terms of the semi-Markov transition function is derived.
scientific article; zbMATH DE number 724096