The Annals of Probability

Stationary distributions for a class of generalized Fleming–Viot processes

Kenji Handa

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Abstract

We identify stationary distributions of generalized Fleming–Viot processes with jump mechanisms specified by certain beta laws together with a parameter measure. Each of these distributions is obtained from normalized stable random measures after a suitable biased transformation followed by mixing by the law of a Dirichlet random measure with the same parameter measure. The calculations are based primarily on the well-known relationship to measure-valued branching processes with immigration.

Article information

Source
Ann. Probab., Volume 42, Number 3 (2014), 1257-1284.

Dates
First available in Project Euclid: 26 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.aop/1395838129

Digital Object Identifier
doi:10.1214/12-AOP829

Mathematical Reviews number (MathSciNet)
MR3189071

Zentralblatt MATH identifier
1296.60226

Subjects
Primary: 60J75: Jump processes
Secondary: 60G57: Random measures

Keywords
Generalized Fleming–Viot process measure-valued branching process stable random measure Dirichlet random measure

Citation

Handa, Kenji. Stationary distributions for a class of generalized Fleming–Viot processes. Ann. Probab. 42 (2014), no. 3, 1257--1284. doi:10.1214/12-AOP829. https://projecteuclid.org/euclid.aop/1395838129


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