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April 1996 A countable representation of the Fleming-Viot measure-valued diffusion
Peter Donnelly, Thomas G. Kurtz
Ann. Probab. 24(2): 698-742 (April 1996). DOI: 10.1214/aop/1039639359


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.


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Peter Donnelly. Thomas G. Kurtz. "A countable representation of the Fleming-Viot measure-valued diffusion." Ann. Probab. 24 (2) 698 - 742, April 1996.


Published: April 1996
First available in Project Euclid: 11 December 2002

zbMATH: 0869.60074
MathSciNet: MR1404525
Digital Object Identifier: 10.1214/aop/1039639359

Primary: 60J25 , 60J70 , 60J80 , 60K35 , 92D10

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

Rights: Copyright © 1996 Institute of Mathematical Statistics


Vol.24 • No. 2 • April 1996
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