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Volume 28, Issue 4
An Almost Sure Central Limit Theorem for Weighted Sums of Mixing Sequences

Guangyu Zou & Yong Zhang

Commun. Math. Res., 28 (2012), pp. 359-366.

Published online: 2021-05

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  • Abstract

In this paper, we prove an almost sure central limit theorem for weighted sums of mixing sequences of random variables without stationary assumptions. We no longer restrict to logarithmic averages, but allow rather arbitrary weight sequences. This extends the earlier work on mixing random variables.

  • Keywords

almost sure central limit theorem, weighted sum, mixing sequence, logarithmic average.

  • AMS Subject Headings

60F15, 60F05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-28-359, author = {Zou , Guangyu and Zhang , Yong}, title = {An Almost Sure Central Limit Theorem for Weighted Sums of Mixing Sequences}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {28}, number = {4}, pages = {359--366}, abstract = {

In this paper, we prove an almost sure central limit theorem for weighted sums of mixing sequences of random variables without stationary assumptions. We no longer restrict to logarithmic averages, but allow rather arbitrary weight sequences. This extends the earlier work on mixing random variables.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19039.html} }
TY - JOUR T1 - An Almost Sure Central Limit Theorem for Weighted Sums of Mixing Sequences AU - Zou , Guangyu AU - Zhang , Yong JO - Communications in Mathematical Research VL - 4 SP - 359 EP - 366 PY - 2021 DA - 2021/05 SN - 28 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19039.html KW - almost sure central limit theorem, weighted sum, mixing sequence, logarithmic average. AB -

In this paper, we prove an almost sure central limit theorem for weighted sums of mixing sequences of random variables without stationary assumptions. We no longer restrict to logarithmic averages, but allow rather arbitrary weight sequences. This extends the earlier work on mixing random variables.

Zou , Guangyu and Zhang , Yong. (2021). An Almost Sure Central Limit Theorem for Weighted Sums of Mixing Sequences. Communications in Mathematical Research . 28 (4). 359-366. doi:
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