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Applying Brownian motion to the study of birth-death chains

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  • Markowsky, Greg

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.

Suggested Citation

  • Markowsky, Greg, 2011. "Applying Brownian motion to the study of birth-death chains," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1173-1178, August.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:8:p:1173-1178
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    Cited by:

    1. Greg Markowsky & José Luis Palacios, 2019. "Symmetry in the Green’s Function for Birth-death Chains," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 841-851, September.

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