Ergodicity and mixing bounds for the Fisher–Snedecor diffusion

We consider the Fisher-Snedecor diffusion; that is, the Kolmogorov-Pearson diffusion with the Fisher-Snedecor invariant distribution. In the non-stationary setting we give explicit quantative rates for the convergence rate of respective finite-dimensional distributions to that of the stationary Fisher-Snedecor diffusion, and for the beta-mixing coefficient of this diffusion. As an application, we prove the law of large numbers and the central limit theorem for additive functionals of the Fisher-Snedecor diffusion and construct P-consistent and asymptotically normal estimators for the parameters of this diffusion given its non-stationary observation.