The Annals of Probability

Wandering Random Measures in the Fleming-Viot Model

Donald A. Dawson and Kenneth J. Hochberg

Full-text: Open access


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.

Article information

Ann. Probab., Volume 10, Number 3 (1982), 554-580.

First available in Project Euclid: 19 April 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 60G57: Random measures
Secondary: 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx] 60J25: Continuous-time Markov processes on general state spaces 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 92A15

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


Dawson, Donald A.; Hochberg, Kenneth J. Wandering Random Measures in the Fleming-Viot Model. Ann. Probab. 10 (1982), no. 3, 554--580. doi:10.1214/aop/1176993767.

Export citation