A note on integrals for birth-death processes
A general integral for birth-death Markov processes until the time of extinction is considered. A closed form expression is provided for the expected value in terms of birth and death rates. 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 simple route for numerical evaluation of the integral variance is also suggested. This is a generalization and correction of an article of \textit{C.M. Hernandez-Suarez} and \textit{C. Castillo-Chavez} [ibid. 161, No.1-2, 95-104 (1999; Zbl 0938.60056)].
scientific article; zbMATH DE number 1563821