Infinitely divisible limit processes for the Ewens sampling formula

G. Jogesh Babu, E. Manstavičius

Research output: Contribution to journalArticle

2 Citations (Scopus)

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

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Ewens Sampling Formula
Infinitely Divisible
Partial Sum Process
Converge
Sums of Independent Random Variables
Population Genetics
Stable Process
Number theory
Partial Sums
Weak Convergence
Function Space
Probability Measure
Counterexample
Finite Set
Permutation
If and only if
Necessary Conditions
Integer
Necessary
Dependent

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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Infinitely divisible limit processes for the Ewens sampling formula. / Babu, G. Jogesh; Manstavičius, E.

In: Lithuanian Mathematical Journal, Vol. 42, No. 3, 01.01.2002, p. 232-242.

Research output: Contribution to journalArticle

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