Infinitely divisible limit processes for the Ewens sampling formula

G. J. Babu, E. Manstavičius

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

The Ewens sampling formula in population genetics can be viewed as a probability measure on the group of permutations of a finite set of integers. Functional limit theory for processes defined through partial sums of dependent variables with respect to the Ewens sampling formula is developed. Using techniques from probabilistic number theory, it is shown that, under very general conditions, a partial sum process weakly converges in a function space if and only if the corresponding process defined through sums of independent random variables weakly converges. As a consequence of this result, necessary and sufficient conditions for weak convergence to a stable process are established. A counterexample showing that these conditions are not necessary for the one-dimensional convergence is presented. Very few results on the necessity part are known in the literature.

Original languageEnglish (US)
Pages (from-to)232-242
Number of pages11
JournalLithuanian Mathematical Journal
Volume42
Issue number3
DOIs
StatePublished - Jan 1 2002

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Infinitely divisible limit processes for the Ewens sampling formula'. Together they form a unique fingerprint.

  • Cite this