On Recurrence, Convergence and Mixing Rate of Generalised Wright\tire Fisher Diffusion with Mutation

R.Yu. Sineokiy, A.Yu. Veretennikov

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


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