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Ethier, S. N.; Kurtz, Thomas G.

Coupling and ergodic theorems for Fleming-Viot processes. (English) Zbl 0940.60045

Ann. Probab. 26, No. 2, 533-561 (1998).
Summary: Fleming-Viot processes are probability-measure-valued diffusion processes that can be used as stochastic models in population genetics. Here we use duality methods to prove ergodic theorems for Fleming-Viot processes, including those with recombination. Coupling methods are also used to establish ergodicity of Fleming-Viot processes, first without and then with selection. A special type of selection known as symmetric overdominance is treated by other methods.

Cited in 2 Reviews
Cited in 9 Documents

MSC:

60F99 Limit theorems in probability theory
60J60 Diffusion processes
60G57 Random measures
92D10 Genetics and epigenetics
60G10 Stationary stochastic processes

Keywords:

ergodicity; stationary distribution; duality; coupling; measure-valued diffusion; population genetics; recombination; selection
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\textit{S. N. Ethier} and \textit{T. G. Kurtz}, Ann. Probab. 26, No. 2, 533--561 (1998; Zbl 0940.60045)
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References:

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[30] SALT LAKE CITY, UTAH 84112 MADISON, WISCONSIN 53706 E-MAIL: ethier@math.utah.edu E-MAIL: kurtz@math.wisc.edu
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