On the law of large numbers for discrete Fourier transform

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• 作者：Na Zhang ^{zhangn4@mail.uc.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 60F15 ; secondary ; 42A20
• 刊名：Statistics & Probability Letters
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：120
• 期：Complete
• 页码：101-107
• 全文大小：362 K

文摘

We shall establish the law of large numbers for the discrete Fourier transform of random variables with finite first moment under condition P(|X_n|>x)≤P(|X₁|>x)$P(\left|X_n\right|>x)\le P(\left|X_1\right|>x)$ for all x≥0$x\ge 0$; for 1<p<2$1<p<2$, we establish the Marcinkiewicz–Zygmund type rate of convergence for the discrete Fourier transform of random variables with finite pth$pth$ moment under condition $\frac{1}{n}{\sum }_{k=1}^{n}P(\left|X_k\right|>x)\le MP(\left|X_1\right|>x)$ for all x≥0$x\ge 0$ and some positive constant M$M$.