On the “birth-and-death” process

Abstract

The “birth-and-death” process is a discontinuous stochastic process in which the stochastic variable, n = 0,1,2,…, can change by only plus one, “birth”, and minus one, “death”. It plays an important role in many practical applications of stochastic processes to biology, physics, and so on. E. g. it has been discussed by Feller (1939), Arley (1943), Arley and Borchsenius (1945), Bartlett (1946) and Kendall (1948).