Time-changed Feller's Brownian motions are birth-death processes

Abstract: The main result of this paper demonstrates that every Feller's Brownian motion, specifically, the Brownian motion with general boundary conditions as examined by Ito and McKean, can be transformed into a birth-death process through a time-change. Additionally, we have derived the parameters of the birth-death processes in terms of those associated with Feller's Brownian motion.