Applying Brownian motion to the study of birth-death chains |
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Authors: | Greg Markowsky |
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Institution: | Monash University, School of Mathematical Sciences, Clayton, Victoria 3800, Australia |
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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. |
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Keywords: | Birth-death chain Markov chain Brownian motion Local time |
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