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Volume 27, Issue 1
Hájek-Rényi-Type Inequality for a Class of Random Variable Sequences and Its Applications

Xuejun Wang, Yan Shen, Shuhe Hu & Wenzhi Yang

Commun. Math. Res., 27 (2011), pp. 6-16.

Published online: 2021-05

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  • Abstract

In this paper, we obtain the Hájek-Rényi-type inequality for a class of random variable sequences and give some applications for associated random variable sequences, strongly positive dependent stochastic sequences and martingale difference sequences which generalize and improve the results of Prakasa Rao and Soo published in Statist. Probab. Lett., 57(2002) and 78(2008). Using this result, we get the integrability of supremum and the strong law of large numbers for a class of random variable sequences.

  • Keywords

Hájek-Rényi-type inequality, associated random variable sequence, strongly positive dependent stochastic sequence, martingale difference sequence.

  • AMS Subject Headings

60F15, 60E15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-27-6, author = {Wang , XuejunShen , YanHu , Shuhe and Yang , Wenzhi}, title = {Hájek-Rényi-Type Inequality for a Class of Random Variable Sequences and Its Applications}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {27}, number = {1}, pages = {6--16}, abstract = {

In this paper, we obtain the Hájek-Rényi-type inequality for a class of random variable sequences and give some applications for associated random variable sequences, strongly positive dependent stochastic sequences and martingale difference sequences which generalize and improve the results of Prakasa Rao and Soo published in Statist. Probab. Lett., 57(2002) and 78(2008). Using this result, we get the integrability of supremum and the strong law of large numbers for a class of random variable sequences.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19102.html} }
TY - JOUR T1 - Hájek-Rényi-Type Inequality for a Class of Random Variable Sequences and Its Applications AU - Wang , Xuejun AU - Shen , Yan AU - Hu , Shuhe AU - Yang , Wenzhi JO - Communications in Mathematical Research VL - 1 SP - 6 EP - 16 PY - 2021 DA - 2021/05 SN - 27 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19102.html KW - Hájek-Rényi-type inequality, associated random variable sequence, strongly positive dependent stochastic sequence, martingale difference sequence. AB -

In this paper, we obtain the Hájek-Rényi-type inequality for a class of random variable sequences and give some applications for associated random variable sequences, strongly positive dependent stochastic sequences and martingale difference sequences which generalize and improve the results of Prakasa Rao and Soo published in Statist. Probab. Lett., 57(2002) and 78(2008). Using this result, we get the integrability of supremum and the strong law of large numbers for a class of random variable sequences.

Wang , XuejunShen , YanHu , Shuhe and Yang , Wenzhi. (2021). Hájek-Rényi-Type Inequality for a Class of Random Variable Sequences and Its Applications. Communications in Mathematical Research . 27 (1). 6-16. doi:
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