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.