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.
Publié le : 1982-08-14
Classification:
Measure-valued Markov process,
random measure,
Hausdorff dimension,
ladder or stepwise-mutation model,
population genetics,
Fleming-Viot model,
wandering coherent distribution,
60G57,
60J70,
60J25,
60K35,
92A15
@article{1176993767,
author = {Dawson, Donald A. and Hochberg, Kenneth J.},
title = {Wandering Random Measures in the Fleming-Viot Model},
journal = {Ann. Probab.},
volume = {10},
number = {4},
year = {1982},
pages = { 554-580},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993767}
}
Dawson, Donald A.; Hochberg, Kenneth J. Wandering Random Measures in the Fleming-Viot Model. Ann. Probab., Tome 10 (1982) no. 4, pp. 554-580. http://gdmltest.u-ga.fr/item/1176993767/