### 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. Techniques from probabilistic number theory are used to establish necessary and sufficient conditions for weak convergence of the associated dependent process to a process with independent increments. Not many results on the necessity part are known in the literature.

Original language | English (US) |
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Pages (from-to) | 607-620 |

Number of pages | 14 |

Journal | Annals of the Institute of Statistical Mathematics |

Volume | 54 |

Issue number | 3 |

DOIs | |

State | Published - Dec 1 2002 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability

### Cite this

*Annals of the Institute of Statistical Mathematics*,

*54*(3), 607-620. https://doi.org/10.1023/A:1022419328971

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*Annals of the Institute of Statistical Mathematics*, vol. 54, no. 3, pp. 607-620. https://doi.org/10.1023/A:1022419328971

**Limit processes with independent increments for the Ewens sampling formula.** / Babu, Gutti Jogesh; Manstavičius, Eugenijus.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Limit processes with independent increments for the Ewens sampling formula

AU - Babu, Gutti Jogesh

AU - Manstavičius, Eugenijus

PY - 2002/12/1

Y1 - 2002/12/1

N2 - 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. Techniques from probabilistic number theory are used to establish necessary and sufficient conditions for weak convergence of the associated dependent process to a process with independent increments. Not many results on the necessity part are known in the literature.

AB - 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. Techniques from probabilistic number theory are used to establish necessary and sufficient conditions for weak convergence of the associated dependent process to a process with independent increments. Not many results on the necessity part are known in the literature.

UR - http://www.scopus.com/inward/record.url?scp=12244262760&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=12244262760&partnerID=8YFLogxK

U2 - 10.1023/A:1022419328971

DO - 10.1023/A:1022419328971

M3 - Article

AN - SCOPUS:12244262760

VL - 54

SP - 607

EP - 620

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

SN - 0020-3157

IS - 3

ER -