On recurrent properties and convergence rates of generalised Fisher -- Wright's diffusion with mutation

TL;DR

This paper studies a generalized Fisher-Wright diffusion process with mutations, proving it is exponentially recurrent and converges rapidly to its invariant distribution, which enhances understanding of its long-term behavior.

Contribution

The paper establishes exponential recurrence and convergence rates for a generalized Fisher-Wright diffusion with mutations, extending previous models in population genetics.

Findings

Proves exponential recurrence of the process

Demonstrates exponential convergence rate to invariant measure

Provides insights into the long-term behavior of the model

Abstract

A generalised one-dimensional Fisher-Wright diffusion process with mutations is considered. This is a well-known model in population genetics. An exponential recurrence is established for the process, which also implies an exponential rate of convergence towards the invariant measure.