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November 2013 Ergodicity and mixing bounds for the Fisher–Snedecor diffusion
A.M. Kulik, N.N. Leonenko
Bernoulli 19(5B): 2294-2329 (November 2013). DOI: 10.3150/12-BEJ453


We consider the Fisher–Snedecor diffusion; that is, the Kolmogorov–Pearson diffusion with the Fisher–Snedecor invariant distribution. In the nonstationary setting, we give explicit quantitative 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 nonstationary observation.


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A.M. Kulik. N.N. Leonenko. "Ergodicity and mixing bounds for the Fisher–Snedecor diffusion." Bernoulli 19 (5B) 2294 - 2329, November 2013.


Published: November 2013
First available in Project Euclid: 3 December 2013

zbMATH: 1296.60215
MathSciNet: MR3160555
Digital Object Identifier: 10.3150/12-BEJ453

Keywords: $\beta$-mixing coefficient , central limit theorem , convergence rate , Fisher–Snedecor diffusion , Law of Large Numbers

Rights: Copyright © 2013 Bernoulli Society for Mathematical Statistics and Probability


Vol.19 • No. 5B • November 2013
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