Abstract:In now classic work, David Kendall (1966) recognized that the Yule process and Poisson process could be related by a (random) time change. Furthermore, he showed that the Yule population size rescaled by its mean has an almost sure exponentially distributed limit as t → ∞. In this note we introduce a class of coupled delayed Yule processes parameterized by 0 < α ≤ 1 that includes the Poisson process at α = 1/2. Moreover we extend Kendall's limit theorem to include a larger class of positive martingales derived… Show more
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.