Convergence rates in the law of large numbers for long-range dependent linear processes

Baum and Katz (Trans. Am. Math. Soc. 120:108-123, 1965) obtained convergence rates in the Marcinkiewicz-Zygmund law of large numbers. Their result has already been extended to the short-range dependent linear processes by many authors. In this paper, we extend the result of Baum and Katz to the long...

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Autores principales: Zhang, Tao, Chen, Pingyan, Sung, Soo Hak
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5624989/
https://www.ncbi.nlm.nih.gov/pubmed/29046604
http://dx.doi.org/10.1186/s13660-017-1517-6
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author Zhang, Tao
Chen, Pingyan
Sung, Soo Hak
author_facet Zhang, Tao
Chen, Pingyan
Sung, Soo Hak
author_sort Zhang, Tao
collection PubMed
description Baum and Katz (Trans. Am. Math. Soc. 120:108-123, 1965) obtained convergence rates in the Marcinkiewicz-Zygmund law of large numbers. Their result has already been extended to the short-range dependent linear processes by many authors. In this paper, we extend the result of Baum and Katz to the long-range dependent linear processes. As a corollary, we obtain convergence rates in the Marcinkiewicz-Zygmund law of large numbers for short-range dependent linear processes.
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spelling pubmed-56249892017-10-16 Convergence rates in the law of large numbers for long-range dependent linear processes Zhang, Tao Chen, Pingyan Sung, Soo Hak J Inequal Appl Research Baum and Katz (Trans. Am. Math. Soc. 120:108-123, 1965) obtained convergence rates in the Marcinkiewicz-Zygmund law of large numbers. Their result has already been extended to the short-range dependent linear processes by many authors. In this paper, we extend the result of Baum and Katz to the long-range dependent linear processes. As a corollary, we obtain convergence rates in the Marcinkiewicz-Zygmund law of large numbers for short-range dependent linear processes. Springer International Publishing 2017-10-02 2017 /pmc/articles/PMC5624989/ /pubmed/29046604 http://dx.doi.org/10.1186/s13660-017-1517-6 Text en © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Zhang, Tao
Chen, Pingyan
Sung, Soo Hak
Convergence rates in the law of large numbers for long-range dependent linear processes
title Convergence rates in the law of large numbers for long-range dependent linear processes
title_full Convergence rates in the law of large numbers for long-range dependent linear processes
title_fullStr Convergence rates in the law of large numbers for long-range dependent linear processes
title_full_unstemmed Convergence rates in the law of large numbers for long-range dependent linear processes
title_short Convergence rates in the law of large numbers for long-range dependent linear processes
title_sort convergence rates in the law of large numbers for long-range dependent linear processes
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5624989/
https://www.ncbi.nlm.nih.gov/pubmed/29046604
http://dx.doi.org/10.1186/s13660-017-1517-6
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AT chenpingyan convergenceratesinthelawoflargenumbersforlongrangedependentlinearprocesses
AT sungsoohak convergenceratesinthelawoflargenumbersforlongrangedependentlinearprocesses

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