Applying Brownian motion to the study of birth-death chains

2011/03/22 by Greg Markowsky, Markowsky, Greg
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1103.4208

openalex publication_date 2011/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Birth-death processes are time-changed Feller's Brownian motions
• An Optional Stopping-like theorem for large stopping times on birth-death chains
• Symmetry in the Green's function for birth-death chains
• Approximation of birth-death processes
• On the mixing time and spectral gap for birth and death chains