Article,
The classification of birth and death processes
Trans. Amer. Math. Soc., (1957)
Abstract
In the applications one is given the matrix A and it is required to con-
structP(t) and to study the propertiesof the corresponding stochastic proc-
ess. 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 resultsof
1 to establish equivalences between properties of the stochastic process
and properties thesequencesXn , n,u and to evaluate,in terms these
of of
sequences, some of the interesting probabilisticquantities associated with the
process.
