Journal of Mathematics of Kyoto University
- J. Math. Kyoto Univ.
- Volume 40, Number 2 (2000), 337-361.
A Fleming-Viot process with unbounded selection
Tachida (1991) proposed a discrete-time model of nearly neutral mutation in which the selection coefficient of a new mutant has a fixed normal distribution with mean 0. The usual diffusion approximation leads to a probability-measure-valued diffusion process, known as a Fleming-Viot process, with the unusual feature of an unbounded selection intensity function. Although the existence of such a diffusion has been proved by Overbeck et al. (1995) using Dirichlet forms, we can now characterize the process via the martingale problem. This leads to a limit theorem justifying the diffusion approximation, using a stronger than usual topology on the state space. Also established are existence, uniqueness, and reversibility of the stationary distribution of the Fleming-Viot process.
J. Math. Kyoto Univ., Volume 40, Number 2 (2000), 337-361.
First available in Project Euclid: 17 August 2009
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] 92D25: Population dynamics (general)
Ethier, Stewart N.; Shiga, Tokuzo. A Fleming-Viot process with unbounded selection. J. Math. Kyoto Univ. 40 (2000), no. 2, 337--361. doi:10.1215/kjm/1250517717. https://projecteuclid.org/euclid.kjm/1250517717