### 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 |

### All Science Journal Classification (ASJC) codes

- Statistics and Probability

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## Cite this

Babu, G. J., & Manstavičius, E. (2002). Limit processes with independent increments for the Ewens sampling formula.

*Annals of the Institute of Statistical Mathematics*,*54*(3), 607-620. https://doi.org/10.1023/A:1022419328971