RANKED MASSES IN TWO-PARAMETER FLEMING-VIOT DIFFUSIONS

被引：1

作者：

Forman, Noah ^{[1
]}

Pal, Soumik ^{[2
]}

Rizzolo, Douglas ^{[3
]}

Winkel, Matthias ^{[4
]}

机构：

[1] McMaster Univ, Dept Math & Stat, 1280 Main St West, Hamilton, ON L8S 4K1, Canada

[2] Univ Washington, Dept Math, Seattle, WA 98195 USA

[3] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

[4] Univ Oxford, Dept Stat, 24-29 St Giles, Oxford OX1 3LB, England

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2023年 / 376卷 / 02期

基金：

加拿大自然科学与工程研究理事会; 英国工程与自然科学研究理事会;

关键词：

Interval partition; Chinese restaurant process; Aldous diffusion; Poisson-Dirichlet distribution; infinitely-many-neutral-alleles model; excursion theory; INFINITE-DIMENSIONAL DIFFUSIONS; DIRICHLET; FAMILY;

D O I：

10.1090/tran/8764

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Previous work constructed Fleming-Viot-type measure-valued diffusions (and diffusions on a space of interval partitions of the unit interval [0, 1]) that are stationary with respect to the Poisson-Dirichlet random measures with parameters alpha is an element of (0, 1) and theta > - alpha. In this paper, we complete the proof that these processes resolve a conjecture by Feng and Sun [Probab. Theory Related Fields 148 (2010), pp. 501-525] by showing that the processes of ranked atom sizes (or of ranked interval lengths) of these diffusions are members of a two-parameter family of diffusions introduced by Petrov [Funct. Anal. Appl. 43 (2009), pp. 279-296], extending a model by Ethier and Kurtz [Adv. in Appl. Probab. 13 (1981), pp. 429-452] in the case alpha = 0.

引用

页码：1089 / 1111

页数：23

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