Infinitely divisible limit processes for the Ewens sampling formula
type: Item
instance of: scholarly article
title: Infinitely divisible limit processes for the Ewens sampling formula
zbMATH Open document ID: 1018.60003
DOI: 10.1023/A:1020265607917
published in: Lithuanian Mathematical Journal
publication date: 2003-05-19T00:00:00Z
review text: This paper is concerned with infinitely divisible limit processes for the Ewens sampling formula. The formula states that if there are no selection effects, the numbers of alleles \(k_1,k_2,\dots,k_n\) represented \(1,2,\dots,n\) times, respectively, in a sample of \(n\) genes are \[ \frac{n!}{v(v+1)\cdots (v+n-1)}\prod^n_{j=1} (v/j)^{k_j}/k_j,\quad v> 0,\;k_j\geq 0, \] where \(k_1 + 2k_2+\cdots nk_n = n\). The authors show that under very general conditions a partial sum process of dependent variables converges weakly in a function space if and only if the corresponding process for independent random variables converges weakly. Necessary and sufficient conditions are established for weak convergence to a stable process, but it is shown by a counterexample that these conditions are not necessary for the one-dimensional convergence.
reviewed by: J. Gani
Mathematics Subject Classification ID: 60B10
Mathematics Subject Classification ID: 60E07
zbMATH DE Number: 1912617
zbMATH Keywords: random partition
zbMATH Keywords: population genetics
zbMATH Keywords: allelic partition
zbMATH Keywords: permutation
zbMATH Keywords: probabilistic number theory
zbMATH Keywords: Skorokhod topology
zbMATH Keywords: functional limit theorem
zbMATH Keywords: stable process
author: G. Jogesh Babu
author: Eugenijus Manstavičius
MaRDI profile type: Publication
full work available at URL: a:1020265607917
OpenAlex ID: W1546079934
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description: scientific article; zbMATH DE number 1912617