The asymptotic behavior of an urn model arising
type: Item
instance of: scholarly article
title: The asymptotic behavior of an urn model arising
zbMATH Open document ID: 0879.60078
DOI: 10.1016/S0304-4149(96)00085-3
published in: Stochastic Processes and their Applications
publication date: 1997-12-10T00:00:00Z
review text: A detailed analysis of asymptotic properties of a Polya-like urn arising in studying stationary distributions and stationary sampling distributions in neutral (Fleming-Viot) genetics models with bounded mutation rates is given. In particular, it is shown that the maximum number of mutations along any lineage from the common ancestor grows extremely slowly with the size of the sample. A similar analysis is applicable to the rate of growth of the number of types in the Ohta-Kimura model (the case in which the mutation process is a simple random walk).
Mathematics Subject Classification ID: 60J75
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 92D10
zbMATH DE Number: 1095915
zbMATH Keywords: Polya urn
zbMATH Keywords: genetics models
zbMATH Keywords: Fleming-Viot process
author: Peter Donnelly
author: Thomas G. Kurtz
MaRDI profile type: Publication
cites work: Q5674726
cites work: A countable representation of the Fleming-Viot measure-valued diffusion
cites work: On the functional central limit theorem for the Ewens sampling formula
cites work: The infinitely-many-sites model as a measure-valued diffusion
cites work: On the stationary distribution of the neutral diffusion model in population genetics
cites work: Fleming–Viot Processes in Population Genetics
cites work: Q3888269
cites work: Genealogical-tree probabilities in the infinitely-many-site model
cites work: Pólya-like urns and the Ewens' sampling formula
cites work: The number of distinguishable alleles according to the Ohta-Kimura model of neutral mutation
cites work: Q3664881
cites work: The coalescent
cites work: Line-of-descent and genealogical processes, and their applications in population genetics models
full work available at URL: s0304-4149(96)00085-3
OpenAlex ID: W1964237833
description: scientific article; zbMATH DE number 1095915