Revisiting the state transition frequency formula

In this paper, we give a new proof of the transition frequency formula for the state transition counting process in a vector Markov process (VMP). The formula was first presented by the author in the early eighties. We also d erive the absorbing distribution, the renewal distribution and the entering probability formulas from the formula. As an application, we use derived r esults to reduce the analysis of a fluid model with random disruptions.