English

Applying Brownian motion to the study of birth-death chains

Probability 2011-03-23 v1

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

Cite

@article{arxiv.1103.4208,
  title  = {Applying Brownian motion to the study of birth-death chains},
  author = {Greg Markowsky},
  journal= {arXiv preprint arXiv:1103.4208},
  year   = {2011}
}

Comments

2 figures