Annals of Probability

Limit theorems for Absorption Times of Genetic Models

S. N. Ethier

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Abstract

We consider a sequence of Markov chains occurring in population genetics (viz., the so-called multiallelic Wright-Fisher models) that converges weakly to a multidimensional diffusion process. Certain absorption times, which arise naturally in connection with the genetic models, are shown to also converge weakly. This extends a result of Guess. Corollaries include convergence of moments of absorption times and convergence of absorption probabilities. The latter results are used implicitly in population genetics.

Article information

Source
Ann. Probab., Volume 7, Number 4 (1979), 622-638.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994986

Digital Object Identifier
doi:10.1214/aop/1176994986

Mathematical Reviews number (MathSciNet)
MR537210

Zentralblatt MATH identifier
0411.60039

JSTOR
links.jstor.org

Subjects
Primary: 60F99: None of the above, but in this section
Secondary: 92A10 60B10: Convergence of probability measures 60J60: Diffusion processes [See also 58J65]

Keywords
Genetic models absorption times weak convergence limiting diffusion martingale problem

Citation

Ethier, S. N. Limit theorems for Absorption Times of Genetic Models. Ann. Probab. 7 (1979), no. 4, 622--638. doi:10.1214/aop/1176994986. https://projecteuclid.org/euclid.aop/1176994986


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