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August, 1982 Wandering Random Measures in the Fleming-Viot Model
Donald A. Dawson, Kenneth J. Hochberg
Ann. Probab. 10(3): 554-580 (August, 1982). DOI: 10.1214/aop/1176993767


Fleming and Viot have established the existence of a continuous-state-space version of the Ohta-Kimura ladder or stepwise-mutation model of population genetics for describing allelic frequencies within a selectively neutral population undergoing mutation and random genetic drift. Their model is given by a probability-measure-valued Markov diffusion process. In this paper, we investigate the qualitative behavior of such measure-valued processes. It is demonstrated that the random measure is supported on a bounded generalized Cantor set and that this set performs a "wandering" but "coherent" motion that, if appropriately rescaled, approaches a Brownian motion. The method used involves the construction of an interacting infinite particle system determined by the moment measures of the process and an analysis of the function-valued process that is "dual" to the measure-valued process of Fleming and Viot.


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Donald A. Dawson. Kenneth J. Hochberg. "Wandering Random Measures in the Fleming-Viot Model." Ann. Probab. 10 (3) 554 - 580, August, 1982.


Published: August, 1982
First available in Project Euclid: 19 April 2007

zbMATH: 0492.60045
MathSciNet: MR659528
Digital Object Identifier: 10.1214/aop/1176993767

Primary: 60G57
Secondary: 60J25 , 60J70 , 60K35 , 92A15

Keywords: Fleming-Viot model , Hausdorff dimension , ladder or stepwise-mutation model , Measure-valued Markov process , Population genetics , random measure , wandering coherent distribution

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 3 • August, 1982
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