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COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF RANDOM ELEMENTS

성수학
대한수학회 (The Korean Mathematical Society)|2010.03|대한수학회보 (Bulletin of the KMS)|제47권 제2호|pp. 369-383

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참고문헌

키워드

weighted sumscomplete convergenceconvergence in probabilityarray of random elementsrowwise independence
주제분류수학

초록

We obtain a result on complete convergence of weighted sums for arrays of rowwise independent Banach space valued random elements. No assumptions are given on the geometry of the underlying Banach space. The result generalizes the main results of Ahmed et al. [1], Chen et al. [2], and Volodin et al. [14].

Abstract

We obtain a result on complete convergence of weighted sums for arrays of rowwise independent Banach space valued random elements. No assumptions are given on the geometry of the underlying Banach space. The result generalizes the main results of Ahmed et al. [1], Chen et al. [2], and Volodin et al. [14].

참고문헌 (15)

  1. S. E. Ahmed, "On the rate of complete convergence for weighted sums of arrays of Banach space valued random elements with application to moving average processes", Statist. Probab. Lett., 58(2), pp.185~194 (2002)
  2. P. Chen, "Rate of complete convergence for arrays of Banach space valued random elements", Siberian Adv. Math., 16(3), pp.1~14 (2006)
  3. A. de Acosta, "Inequalities for B-valued random vectors with applications to the strong law of large numbers", Ann. Probab., 9(1), pp.157~161 (1981)
  4. P. L. Hsu, "Complete convergence and the law of large numbers", Proc. Nat. Acad. Sci. U. S. A., 33, pp.25~31 (1947)
  5. T.-C. Hu, "On the rate of complete convergence for weighted sums of arrays of Banach space valued random elements", Teor. Veroyatnost. i Primenen., 47(3), pp.533~547 (2003)
  6. T.-C. Hu, "On complete convergence for arrays of rowwise independent random elements in Banach spaces", Stochastic Anal. Appl., 17(6), pp.963~992 (1999)
  7. A. Kuczmaszewska, "On complete convergence in a Banach space", Internat. J. Math. Math. Sci., 17(1), pp.1~14 (1994)
  8. J. Kuelbs, "Some stability results for vector valued random variables", Ann. Probab., 7(1), pp.75~84 (1979)
  9. M. Ledoux, "Probability in Banach Spaces" (1991), Springer-Verlag
  10. S. H. Sung, "Complete convergence for weighted sums of arrays of rowwise independent B-valued random variables", Stochastic Anal. Appl., 15(2), pp.255~267 (1997)
  11. S. H. Sung, "Complete convergence for weighted sums of random variables", Statist. Probab. Lett., 77(3), pp.303~311 (2007)
  12. 성수학, "On complete convergence for arrays of rowwise independent random elements", 대한수학회지, 44(2), pp.467~476 (2007), 대한수학회
  13. 성수학, "On the rate of complete convergence for weighted sums of arrays of random elements", 대한수학회지, 43(4), pp.815~828 (2006), 대한수학회
  14. A. Volodin, "A note on the rate of complete convergence for weighted sums of arrays of Banach space valued random elements", Lobachevskii J. Math., 15, pp.21~33 (2004)
  15. X. Wang, "Convergence rates on strong laws of large numbers for arrays of rowwise independent elements", Stochastic Anal. Appl., 11(1), pp.115~132 (1993)

관련 논문AI추천

On the complete convergence for arrays of rowwise extended negatively dependent random variablesAndrei Volodin, Dehua Qiu, Pingyan Chen, Rita Giuliano Antonini대한수학회 · 대한수학회지2013 · 제50권 제2호On the rate of complete convergence for weighted sums of arrays of random elements성수학, Andrei I. Volodin대한수학회 · 대한수학회지2006 · 제43권 제4호A NOTE ON THE COMPLETE MOMENT CONVERGENCE FOR ARRAYS OF B-VALUED RANDOM VARIABLESMingzhu Song, YongFeng Wu대한수학회 · 대한수학회보2015 · 제52권 제3호MEAN CONVERGENCE THEOREMS AND WEAK LAWS OF LARGE NUMBERS FOR DOUBLE ARRAYS OF RANDOM ELEMENTS IN BANACH SPACESLe Van Dung, Nguyen Duy Tien대한수학회 · 대한수학회보2010 · 제47권 제3호Complete convergence and complete moment convergence theorems for weighted sums of arrays of rowwise extended negatively dependent random variablesHaiwu Huang, Qingxia Zhang대한수학회 · 대한수학회보2019 · 제56권 제4호On the complete convergence for weighted sums of dependent random variables under condition of weighted integrabilityJong-Il Baek, Mi-Hwa Ko, Tae-Sung Kim대한수학회 · 대한수학회지2008 · 제45권 제4호

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