On recurrent properties of Fisher-Wright's diffusion on $(0,1)$ with mutation

TL;DR

This paper investigates the exponential recurrence and convergence rate of the Fisher-Wright diffusion process with mutations, a key model in population genetics, on the interval (0,1).

Contribution

It establishes exponential recurrence and convergence rates for the Fisher-Wright diffusion with mutations, enhancing understanding of its long-term behavior.

Findings

Proves exponential recurrence of the process.

Establishes exponential convergence rate to the invariant measure.

Provides insights into the long-term stability of the model.

Abstract

One-dimensional Fisher-Wright diffusion process on the interval $(0,1)$ with mutations is considered. This is a widely known model in population genetics. The goal of the paper is an exponential recurrence of the process, which also implies exponential rate of convergence towards the invariant measure.