Bernoulli

  • Bernoulli
  • Volume 19, Number 5B (2013), 2294-2329.

Ergodicity and mixing bounds for the Fisher–Snedecor diffusion

A.M. Kulik and N.N. Leonenko

Full-text: Open access

Abstract

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.

Article information

Source
Bernoulli Volume 19, Number 5B (2013), 2294-2329.

Dates
First available in Project Euclid: 3 December 2013

Permanent link to this document
https://projecteuclid.org/euclid.bj/1386078604

Digital Object Identifier
doi:10.3150/12-BEJ453

Mathematical Reviews number (MathSciNet)
MR3160555

Zentralblatt MATH identifier
1296.60215

Keywords
$\beta$-mixing coefficient central limit theorem convergence rate Fisher–Snedecor diffusion law of large numbers

Citation

Kulik, A.M.; Leonenko, N.N. Ergodicity and mixing bounds for the Fisher–Snedecor diffusion. Bernoulli 19 (2013), no. 5B, 2294--2329. doi:10.3150/12-BEJ453. https://projecteuclid.org/euclid.bj/1386078604.


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