%0 Journal Article %1 dawson1982wandering %A Dawson, Donald A. %A Hochberg, Kenneth J. %D 1982 %I The Institute of Mathematical Statistics %J The Annals of Probability %K Fleming_Viot coalescent_theory duality lookdown_process spatial_coalescent %N 3 %P 554--580 %R 10.1214/aop/1176993767 %T Wandering Random Measures in the Fleming-Viot Model %U http://dx.doi.org/10.1214/aop/1176993767 %V 10 %X 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 descrbing 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 Brownian motion. The method used invovles 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{dawson1982wandering, abstract = {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 descrbing 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 Brownian motion. The method used invovles 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.}, added-at = {2014-05-27T19:51:32.000+0200}, ajournal = {Ann. Probab.}, author = {Dawson, Donald A. and Hochberg, Kenneth J.}, biburl = {https://www.bibsonomy.org/bibtex/2b8e933ecc43a6024854fbe42b5bf92ae/peter.ralph}, doi = {10.1214/aop/1176993767}, interhash = {969812e028b385770632a7bb69f73b69}, intrahash = {b8e933ecc43a6024854fbe42b5bf92ae}, journal = {The Annals of Probability}, keywords = {Fleming_Viot coalescent_theory duality lookdown_process spatial_coalescent}, month = {08}, number = 3, pages = {554--580}, publisher = {The Institute of Mathematical Statistics}, timestamp = {2014-09-14T17:43:51.000+0200}, title = {Wandering Random Measures in the {Fleming-Viot} Model}, url = {http://dx.doi.org/10.1214/aop/1176993767}, volume = 10, year = 1982 }