The Annals of Probability

A countable representation of the Fleming-Viot measure-valued diffusion

Peter Donnelly and Thomas G. Kurtz

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Abstract

The Fleming-Viot measure-valued diffusion arises as the infinite population limit of various discrete genetic models with general type space. The paper gives a countable construction of the process as the empirical measure carried by a certain interactive particle system. This explicit representation facilitates the study of various properties of the Fleming-Viot process. The construction also carries versions of the familiar genealogical processes from population genetics, in particular, Kingman's coalescent, thus unifying the genealogical and measure-valued approaches to the subject.

Article information

Source
Ann. Probab., Volume 24, Number 2 (1996), 698-742.

Dates
First available in Project Euclid: 11 December 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1039639359

Digital Object Identifier
doi:10.1214/aop/1039639359

Mathematical Reviews number (MathSciNet)
MR1404525

Zentralblatt MATH identifier
0869.60074

Subjects
Primary: 60J25: Continuous-time Markov processes on general state spaces 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx] 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 92D10: Genetics {For genetic algebras, see 17D92}

Keywords
Fleming-Viot process measure-valued diffusion exchangeability coupling sample-path properties ergodicity genealogical processes the coalescent

Citation

Donnelly, Peter; Kurtz, Thomas G. A countable representation of the Fleming-Viot measure-valued diffusion. Ann. Probab. 24 (1996), no. 2, 698--742. doi:10.1214/aop/1039639359. https://projecteuclid.org/euclid.aop/1039639359


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  • UNITED KINGDOM MADISON, WISCONSIN 53706-1388 E-MAIL: p.j.donnelly@qmw.ac.uk E-MAIL: kurtz@math.wisc.edu