Applying Brownian motion to the study of birth-death chains

Details Applying Brownian motion to the study of birth-death chains Applying Brownian motion to the study of birth-death chains

2011-03-22

arxiv.org/abs/1103.4208v1

Mathematics

Probability

2 figures

Scientific paper

Basic properties of Brownian motion are used to derive two results concerning birth-death chains. First, the probability of extinction is calculated. Second, sufficient conditions on the transition probabilities of a birth-death chain are given to ensure that the expected value of the chain converges to a limit. The theory of Brownian motion local time figures prominently in the proof of the second result.

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