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Theory of Probability and Mathematical Statistics

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Non-central limit theorems and convergence rates


Authors: Vo Anh, Andriy Olenko and V. Vaskovych
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 95 (2016).
Journal: Theor. Probability and Math. Statist. 95 (2017), 3-15
MSC (2010): Primary 60G60, 60F05, 60G12
DOI: https://doi.org/10.1090/tpms/1019
Published electronically: February 28, 2018
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Abstract: This paper surveys some recent developments in non-central limit theorems for long-range dependent random processes and fields. We describe an increasing domain framework for asymptotic behavior of functionals of random processes and fields. Recent results on the rate of convergence to the Hermite-type distributions in non-central limit theorems are presented. The use of these results is demonstrated through an application to the case of Rosenblatt-type distributions.


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Additional Information

Vo Anh
Affiliation: School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, 4001, Australia
Email: v.anh@qut.edu.au

Andriy Olenko
Affiliation: Department of Mathematics and Statistics, La Trobe University, Melbourne, Victoria, 3086, Australia
Email: a.olenko@latrobe.edu.au

V. Vaskovych
Affiliation: Department of Mathematics and Statistics, La Trobe University, Melbourne, Victoria, 3086, Australia
Email: vaskovych.v@students.latrobe.edu.au

DOI: https://doi.org/10.1090/tpms/1019
Keywords: Non-central limit theorems, rate of convergence, random field, long-range dependence, Rosenblatt-type distributions
Received by editor(s): September 27, 2016
Published electronically: February 28, 2018
Additional Notes: The first author was supported in part under the Australian Research Council’s Discovery Projects funding scheme (project number DP160101366)
The second author was supported in part under the Australian Research Council’s Discovery Projects funding scheme (project number DP160101366) and by the La Trobe University DRP Grant in Mathematical and Computing Sciences
Dedicated: This paper is dedicated to Professor N.N. Leonenko on the occasion of his 65th birthday
Article copyright: © Copyright 2018 American Mathematical Society

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