The Annals of Probability

The Transition Function of a Fleming-Viot Process

S. N. Ethier and R. C. Griffiths

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Abstract

Let $S$ be a compact metric space, let $\theta \geq 0$, and let $\nu_0$ be a Borel probability measure on $S$. An explicit formula is found for the transition function of the Fleming-Viot process with type space $S$ and mutation operator $(Af)(x) = (1/2)\theta\int_S(f(\xi) - f(x))\nu_0(d\xi)$.

Article information

Source
Ann. Probab., Volume 21, Number 3 (1993), 1571-1590.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176989131

Digital Object Identifier
doi:10.1214/aop/1176989131

Mathematical Reviews number (MathSciNet)
MR1235429

Zentralblatt MATH identifier
0778.60038

JSTOR
links.jstor.org

Subjects
Primary: 60G57: Random measures
Secondary: 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07] 60J60: Diffusion processes [See also 58J65] 92D15: Problems related to evolution

Keywords
Infinite-dimensional diffusion process measure-valued diffusion Poisson-Dirichlet distribution infinitely-many-neutral-alleles diffusion model population genetics

Citation

Ethier, S. N.; Griffiths, R. C. The Transition Function of a Fleming-Viot Process. Ann. Probab. 21 (1993), no. 3, 1571--1590. doi:10.1214/aop/1176989131. https://projecteuclid.org/euclid.aop/1176989131


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