Limit theorems for Absorption Times of Genetic Models

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.