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An inequality of widely dependent random variables and its applications*

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Abstract

In this paper, we prove a more accurate inequality of widely dependent random variables. Based on this inequality, we obtain some limit theorems for widely dependent random variables, which expand ranges of dominating coefficients, thereby expanding scopes of applications of the obtained limit theorems. These limit theorems include the strong law of large numbers, the complete convergence, the a.s. elementary renewal theorem, and the weighted elementary renewal theorem.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Yili Normal University, Yining, 835000, China

    Wei Chen

  2. School of Mathematical Sciences, Soochow University, Suzhou, 215006, China

    Yuebao Wang & Dongya Cheng

Authors
  1. Wei Chen
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  2. Yuebao Wang
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  3. Dongya Cheng
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Corresponding author

Correspondence to Yuebao Wang.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 11071082, 11401415), Natural Science Foundation of the Higher Education Institutions of Jiangsu Province, China (No. 13KJB110025), and Postdoctoral Research Program of Jiangsu Province of China (No. 1402111C).

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Chen, W., Wang, Y. & Cheng, D. An inequality of widely dependent random variables and its applications*. Lith Math J 56, 16–31 (2016). https://doi.org/10.1007/s10986-016-9301-8

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  • DOI: https://doi.org/10.1007/s10986-016-9301-8

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