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In this paper, the complete convergence and complete moment convergence for a class of random variables satisfying the Rosenthal type inequality are investigated. The sufficient and necessary conditions for the complete convergence and complete moment convergence are provided. As applications, the Baum-Katz type result and the Marcinkie\-wicz-Zygmund type strong law of large numbers for a class of random variables satisfying the Rosenthal type inequality are established. The results obtained in the paper extend the corresponding ones for some dependent random variables.
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참고문헌 (23)
참고문헌 신청
A. T. Shen / 2013 / Complete convergence of the maximum partial sums for arrays of rowwise of AANA random variables / Discrete Dyn. Nat. Soc 2013 : 7 ~
A. T. Shen / 2014 / On asymptotic approximation of inverse moments for a class of nonnegative random variables / Statistics 48 (6) : 1371 ~ 1379
A. T. Shen / 2014 / Strong convergence for sequences of asymptotically almost negatively associated random variables / Stochastic 86 (2) : 291 ~ 303
A. T. Shen / 2015 / Applications of the Rosenthal-type inequality for negatively superadditive dependent random variables / Metrika 78 (3) : 295 ~ 311
D. M. Yuan / 2009 / Rosenthal type inequalities for asymptotically almost negatively associated random variables and applications / Sci. China Ser. A 52 (9) : 1887 ~ 1904
A. T. Shen / 2014 / On asymptotic approximation of inverse moments for a class of nonnegative random variables / Statistics 48 (6) : 1371 ~ 1379
A. T. Shen / 2014 / Strong convergence for sequences of asymptotically almost negatively associated random variables / Stochastic 86 (2) : 291 ~ 303
A. T. Shen / 2015 / Applications of the Rosenthal-type inequality for negatively superadditive dependent random variables / Metrika 78 (3) : 295 ~ 311
D. M. Yuan / 2009 / Rosenthal type inequalities for asymptotically almost negatively associated random variables and applications / Sci. China Ser. A 52 (9) : 1887 ~ 1904
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