On Recurrence, Convergence and Mixing Rate of Generalised Wright\tire Fisher Diffusion with Mutation
2023, v.29, Issue 2, 241-258
A generalised one-dimensional Wright\tire Fisher diffusion process with mutations is considered. It describes a well-known population genetics model. An exponential recurrence and exponential convergence towards a unique invariant measure are established under minimal regularity conditions of the coefficients. A non-uniform exponential bound for the beta-mixing coefficient is also obtained.
Keywords: Wright -- Fisher's diffusion; exponential recurrence; beta-mixing