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August, 1979 Limit theorems for Absorption Times of Genetic Models
S. N. Ethier
Ann. Probab. 7(4): 622-638 (August, 1979). DOI: 10.1214/aop/1176994986

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.

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S. N. Ethier. "Limit theorems for Absorption Times of Genetic Models." Ann. Probab. 7 (4) 622 - 638, August, 1979. https://doi.org/10.1214/aop/1176994986

Information

Published: August, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0411.60039
MathSciNet: MR537210
Digital Object Identifier: 10.1214/aop/1176994986

Subjects:
Primary: 60F99
Secondary: 60B10 , 60J60 , 92A10

Keywords: absorption times , Genetic models , Limiting diffusion , Martingale problem , weak convergence

Rights: Copyright © 1979 Institute of Mathematical Statistics

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Vol.7 • No. 4 • August, 1979
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