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Theory of Probability and Mathematical Statistics

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On exponential bounds for mixing and the rate of convergence for Student processes


Authors: N. Abourashchi and A. Yu. Veretennikov
Translated by: The authors
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 81 (2010).
Journal: Theor. Probability and Math. Statist. 81 (2010), 1-13
MSC (2010): Primary 60H10, 60J60
Published electronically: January 14, 2011
MathSciNet review: 2667305
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Abstract | References | Similar Articles | Additional Information

Abstract: Exponential bounds for the $ \beta$-mixing coefficient are established for the Student diffusion process. The latter is a Markov diffusion process with Student distribution as a stationary measure. The method is based on a direct estimation of moments and on polynomial Lyapunov functions for evaluating exponential functionals of hitting times.


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Additional Information

N. Abourashchi
Affiliation: School of Mathematics, University of Leeds, LS2 9JT Leeds, United Kingdom
Email: niloufar@leeds.ac.uk

A. Yu. Veretennikov
Affiliation: Institute for Information Transmission Problems, Moscow, Russia
Address at time of publication: School of Mathematics, University of Leeds, LS2 9JT Leeds, United Kingdom
Email: A.Veretennikov@leeds.ac.uk

DOI: https://doi.org/10.1090/S0094-9000-2010-00805-2
Keywords: Student diffusion, exponential mixing, heavy tails
Received by editor(s): May 28, 2009
Published electronically: January 14, 2011
Article copyright: © Copyright 2010 American Mathematical Society