Large deviation results for a class of Markov chains arising from population genetics
type: Item
instance of: scholarly article
title: Large deviation results for a class of Markov chains arising from population genetics
zbMATH Open document ID: 0684.60018
author: Gregory J. Morrow
author: Stanley A. Sawyer
published in: The Annals of Probability
publication date: 1989-01-01T00:00:00Z
review text: Consider stationary Markov chains \((X^ N_ n)_{n\in {\mathbb{N}}}\) on a bounded subset of \({\mathbb{R}}^ d\) depending on a parameter \(N\in {\mathbb{N}}\) with \(E_ x(X^ N_ 1)=:f_ N(x)\). Let \(x_ 0\) be a common stable fixed point of the functions \(f_ N\) and D an open neighborhood of \(x_ 0\). Assume that N \(cov_ x(X^ N_ 1)\) is bounded away from 0 and \(\infty\) uniformly in \(N\in {\mathbb{N}}\) and \(x\in D.\) Under various regularity assumptions it is proved that the asymptotics (N\(\to \infty)\) of the mean exit times from D and the invariant measures are governed by a quasi-potential as in {\S} 4.4 of \textit{M. I. Frejdlin} and \textit{A. D. Venttsel'}, Random perturbations of dynamical systems (1984; Zbl 0522.60055). The results apply to the Wright-Fisher model in populations genetics.
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 92D10
Mathematics Subject Classification ID: 60G40
zbMATH DE Number: 4121126
zbMATH Keywords: stable fixed point
zbMATH Keywords: invariant measures
zbMATH Keywords: Random perturbations
zbMATH Keywords: Wright- Fisher model
zbMATH Keywords: populations genetics
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176991260
OpenAlex ID: W2017503591
DOI: 10.1214/AOP/1176991260
description: scientific article; zbMATH DE number 4121126