The classification of birth and death processes

In the applications one is given the matrix A and it is required to construct P (t) and to study the properties of the corresponding stochastic process. The existence, uniqueness, and the analytic properties of P (t) have been discussed in detail in I. The objective of this paper is to use the results of 1 to establish equivalences between properties of the stochastic process and properties of the sequences Xn, n, u and to evaluate, in terms of these sequences, some of the interesting probabilistic quantities associated with the process.