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MARCINKIEWICZ-ZYGMUND LAW OF LARGE NUMBERS FOR BLOCKWISE ADAPTED SEQUENCES

  • Published : 2006.02.01

Abstract

In this paper we establish the Marcinkiewicz-Zygmund strong law of large numbers for blockwise adapted sequences. Some related results are considered.

Keywords

References

  1. B. von Bahr and C. G. Esseen, Inequalities for the r-th absolute moment of a sum of random variables, $1{\leq}r{\leq}2$, Ann. Math. Statist. 36 (1965), 299-303 https://doi.org/10.1214/aoms/1177700291
  2. B. D. Choi and S. H. Sung, On convergence of $(S_{n}-ES_{n})/n^{1/r}$, 1 < r < 2, for pairwise independent random variables, Bull. Korean Math. Soc. 22 (1985), no. 2, 79-82
  3. N. Etemadi, An elementary proof of the strong law of large numbers, Z. Wahrsch. Verw. Gebiete 55 (1981), no. 1, 119-122 https://doi.org/10.1007/BF01013465
  4. V. F. Gaposhkin, On the strong law of large numbers for blockwise-independent and blockwise-orthogonal random variables, Theory Probab. Appl. 39 (1994), no. 4, 677-684 https://doi.org/10.1137/1139053
  5. V. F. Gaposhkin, Series of block-orthogonal and block-independent systems, Izv. Vyssh. Uchebn. Zaved. Mat. (1990), no. 5, 12-18
  6. D. H. Hong and S. Y. Hwang, Marcinkiewicz-type Strong law of large numbers for double arrays of pairwise independent random variables, Int. J. Math. Math. Sci. 22 (1999), no. 1, 171-177 https://doi.org/10.1155/S0161171299221710
  7. D. H. Hong and A. I. Volodin, Marcinkiewicz-type law of large numbers for double array, J. Korean Math. Soc. 36 (1999), no. 6, 1133-1143
  8. F. Moricz, Strong limit theorems for blockwise m-independent and blockwise quasi- orthogonal sequences of random variables, Proc. Amer. Math. Soc. 101 (1987), no. 4, 709-715

Cited by

  1. Strong laws for blockwise martingale difference arrays in Banach spaces vol.31, pp.4, 2010, https://doi.org/10.1134/S1995080210040037
  2. Marcinkiewicz-Zygmund type law of large numbers for double arrays of random elements in Banach spaces vol.30, pp.4, 2009, https://doi.org/10.1134/S1995080209040118