ON COMPLETE CONVERGENCE AND COMPLETE MOMENT CONVERGENCE FOR A CLASS OF RANDOM VARIABLES
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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.
Abstract
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.
참고문헌 (23)
- K. Alam, "Positive dependence in multivariate distributions", Comm. Statist. Theory Methods, 10(12), pp.1183~1196 (1981)
- Z. D. Bai, "The complete convergence for partial sums of i.i.d. random vari-ables", Sci. Sinica Ser. A, 28(12), pp.1261~1277 (1985)
- L. E. Baum, "Convergence rates in the law of large numbers", Trans. Amer. Math. Soc, 120(1), pp.108~123 (1965)
- T. K. Chandra, "Extensions of the strong law of large numbers of Marcinkiewicz and Zygmund for dependent variables", Acta Math. Hungar, 71(4), pp.327~336 (1996)
- Z. Y. Chen, "Strong laws of large numbers for weighted sums of asymptotically almost negatively associated random variables", Rev. R. Acad. Cienc. Exactas Fıs. Nat. Ser. A Math. RACSAM, 109(1), pp.135~152 (2015)
- Y. S. Chow, "On the rate of moment complete convergence of sample sums and extremes", Bull. Inst. Math. Acad. Sinica, 16(3), pp.177~201 (1988)
- P. Erdos, "On a theorem of Hsu and Robbins", Ann. Math. Statist, 20, pp.286~291 (1949)
- P. Hsu, "Complete convergence and the law of large numbers", Proceedings of the National Academy of Sciences, 33, pp.25~31 (1947)
- X. Hu, "Strong convergence properties for asymptotically almost negatively associated sequence", Discrete Dyn. Nat. Soc, 2012, pp.8~ (2012)
- K. Joag-Dev, "Negative association of random variables with applica-tions", Ann. Statist, 11(1), pp.286~295 (1983)
- A. T. Shen, "On asymptotic approximation of inverse moments for a class of nonnegative random variables", Statistics, 48(6), pp.1371~1379 (2014)
- A. T. Shen, "Strong convergence for sequences of asymptotically almost negatively associated random variables", Stochastic, 86(2), pp.291~303 (2014)
- A. T. Shen, "Complete convergence of the maximum partial sums for arrays of rowwise of AANA random variables", Discrete Dyn. Nat. Soc, 2013, pp.7~ (2013)
- A. T. Shen, "Applications of the Rosenthal-type inequality for negatively superadditive dependent random variables", Metrika, 78(3), pp.295~311 (2015)
- S. H. Sung, "Moment inequalities and complete moment convergence", J. Inequal. Appl, 2009, pp.14~ (2009)
- X. J. Wang, "Complete convergence for arrays of rowwise asymptotically almost negatively associated random variables", Discrete Dyn. Nat. Soc, 2011, pp.11~ (2011)
- X. H. Wang, "A note on complete convergence of weighted sums for array of rowwise AANA random variables", J. Inequal. Appl, 2013, pp.13~ (2013)
- Y. B. Wang, "The strong law of large numbers and the law of iterated logarithm for product sums of NA and AANA random variables", Southeast Asian Bull. Math, 27(2), pp.369~384 (2003)
- Q. Y. Wu, "Probability Limit Theory for Mixing Sequences" (2006), Science Press of China
- W. Z. Yang, "On complete convergence of moving average process for AANA sequence", Discrete Dyn. Nat. Soc, 2012, pp.24~ (2012)
- D. M. Yuan, "Rosenthal type inequalities for asymptotically almost negatively associated random variables and applications", Sci. China Ser. A, 52(9), pp.1887~1904 (2009)
- D. M. Yuan, "Laws of large numbers for Cesaro alpha-integrable random variables under dependence condition AANA or AQSI", Acta Math. Sin. (Engl. Ser.), 28(6), pp.1103~1118 (2012)
- X. C. Zhou, "Complete moment convergence of moving average processes under φ-mixing assumptions", Statist. Probab. Lett, 80(5-6), pp.285~292 (2010)
