长程相依线性过程大数定律中的收敛速度。
Convergence rates in the law of large numbers for long-range dependent linear processes.
作者信息
Zhang Tao, Chen Pingyan, Sung Soo Hak
机构信息
Department of Statistics, Jinan University, Guangzhou, 510630 P.R. China.
Department of Mathematics, Jinan University, Guangzhou, 510630 P.R. China.
出版信息
J Inequal Appl. 2017;2017(1):241. doi: 10.1186/s13660-017-1517-6. Epub 2017 Oct 2.
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.
鲍姆和卡茨（《美国数学会会刊》120:108 - 123，1965年）在马尔钦凯维奇 - 齐格蒙德大数定律中得到了收敛速度。他们的结果已经被许多作者推广到短程相依线性过程。在本文中，我们将鲍姆和卡茨的结果推广到长程相依线性过程。作为推论，我们得到了短程相依线性过程在马尔钦凯维奇 - 齐格蒙德大数定律中的收敛速度。
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