Applying Brownian motion to the study of birth-death chains

Greg Markowsky

Statistics & Probability Letters, 2011, vol. 81, issue 8, 1173-1178

Abstract: 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.

Keywords: Birth-death; chain; Markov; chain; Brownian; motion; Local; time (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (1)

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