On the Limiting Joint Distribution of Semi-Markov Processes with Finite Number of States, with an Application

We derive expressions for lim_{t → ∞} Prob {Z_t = i, Z_t+z = j} for a semi-Markov process with a finite number of states. As an application of the resuts, we obtain the autocorrelation function of the process of recorded current flowing through a single channel, for two Markovian models of the behavior of drug-operated ion-channels. The additional information provided by the autocorrelation function would facilitate the task of identifying the model which is more consistent with the observed record.