A basic result on the integral for birth-death Markov processes (Q1808682)

This paper is concerned with the expectation of the integral under the stochastic path of a birth-death Markov process until its time of extinction. It also considers the expected time to extinction. The argument used is a regenerative one. Several examples are provided: the M/M/1 queue, the M/M/\(\infty\) queue, the linear birth-death process, and the stochastic logistics SIS epidemic. A table of values for both the integral under the path until extinction, and the expected time to extinction in the SIS epidemic is provided for different values of the birth and death parameters. The paper concludes with two appendices and a list of 22 references.