The renewal equation for the non-homogeneous semi-Markov renewal processes (Q799039)

In the theory of classical semi-Markov processes the distribution of the time which the process stays in the given state is common for all steps of the process. In this paper we consider such semi-Markov processes for which the occupation time in the given state depends also on the moment in which the process transients in this state. For these processes the renewal equation is constructed and the conditions of existence and uniqueness of the solution are also given.