| Some Convergence Properties for $\psi$-Mixing Sequences |
| Received:June 20, 2009 Revised:May 28, 2010 |
| Key Words:
Kolmogorov-type inequality Khintchine-Kolmogorov-type convergence theorem strong law of large numbers.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.\,10871001), Provincial Natural Science Research Project of Anhui Colleges (Grant No.\,KJ2010A005), Talents Youth Fund of Anhui Province Universities (Grant No.\,2010SQRL016ZD), Youth Science Research Fund of Anhui University (Grant No.\,2009QN011A) and the Academic innovation team of Anhui University (Grant No.\,KJTD001B). |
| Author Name | Affiliation | | Xue Jun WANG | School of Mathematical Science, Anhui University, Anhui 230039, P. R. China | | Shu He HU | School of Mathematical Science, Anhui University, Anhui 230039, P. R. China | | Xiao Qin LI | School of Mathematical Science, Anhui University, Anhui 230039, P. R. China | | Wen Zhi YANG | School of Mathematical Science, Anhui University, Anhui 230039, P. R. China |
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| Abstract: |
| In this paper, we extend the Kolmogorov-type inequality to the case of $\psi$-mixing sequences. Moreover, we study the strong limit theorems for partial sums of $\psi$-mixing random variables. As a result, we extend the Khintchine-Kolmogorov-type convergence theorem, the three series theorem, Marcinkiewicz strong law of large number to the case of $\psi$-mixing sequences. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.03.008 |
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