## Journal of Mathematics of Kyoto University

### A Fleming-Viot process with unbounded selection

#### Abstract

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.

#### Article information

Source
J. Math. Kyoto Univ., Volume 40, Number 2 (2000), 337-361.

Dates
First available in Project Euclid: 17 August 2009

https://projecteuclid.org/euclid.kjm/1250517717

Digital Object Identifier
doi:10.1215/kjm/1250517717

Mathematical Reviews number (MathSciNet)
MR1787875

Zentralblatt MATH identifier
0979.92028

#### Citation

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