Large deviation results for a class of Markov chains with application to an infinite alleles model of population genetics
type: Item
instance of: scholarly article
title: Large deviation results for a class of Markov chains with application to an infinite alleles model of population genetics
zbMATH Open document ID: 0767.92019
author: Gregory J. Morrow
published in: The Annals of Applied Probability
publication date: 1993-02-22T00:00:00Z
review text: Let \(\{X_ n^{(N)}\}\) be a Markov chain in the probability measures \(P[0,1]\). Define the exit time \(T=\inf\{n: X_ n\neq D\}\) for some open ball \(D\) once \(X_ 0\in D\). Assuming various regularity conditions it is shown that the expected time \(T\) is logarithmically equivalent to \(\exp\{M(N)V\}\) for some \(M(N)\to \infty\), \(V > 0\). These results apply to an infinite alleles model in population genetics. The present paper is in turn an extension of the work of \textit{G. J. Morrow} and \textit{S. Sawyer} [see Ann. Probab. 17, No. 3, 1124-1146 (1989; Zbl 0684.60018)], where an \(R^ d\)-valued Markov chain was considered.
Mathematics Subject Classification ID: 92D10
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60J10
Mathematics Subject Classification ID: 60J05
zbMATH DE Number: 120357
zbMATH Keywords: topology of weak convergence
zbMATH Keywords: limit of solutions
zbMATH Keywords: variational problems of Wentzell-Freidlin type
zbMATH Keywords: randomly mating genes
zbMATH Keywords: mutation
zbMATH Keywords: selection
zbMATH Keywords: measure-valued Markov chain
zbMATH Keywords: exit time
zbMATH Keywords: expected time
zbMATH Keywords: infinite alleles models
zbMATH Keywords: population genetics
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1177005579
OpenAlex ID: W2029113433
DOI: 10.1214/AOAP/1177005579
description: scientific article; zbMATH DE number 120357