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Weak convergence of the simple birth-and-death process
Published online by Cambridge University Press: 14 July 2016
Abstract
The existence of a weak limit birth-and-death process on the natural integers for the simple birth-and-death process conditional on non-extinction up to time t as t→∞ is proved. Starting from the latter a new weak limiting procedure yields a diffusion Markov process on the positive infinite semi-axis.
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- Copyright © Applied Probability Trust
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