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Moment conditions for almost sure convergence of weakly correlated random variables

Authors: W. Bryc and W. Smoleński
Journal: Proc. Amer. Math. Soc. 119 (1993), 629-635
MSC: Primary 60F15; Secondary 60E15
MathSciNet review: 1149969
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Abstract: For random sequences with unrestricted maximal correlation coefficient strictly less than $ 1$, sufficient moment conditions for almost sure convergence of a series and for the strong law of large numbers are given.

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  • [1] Patrick Billingsley, Convergence of probability measures, John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0233396
  • [2] Richard C. Bradley, On the spectral density and asymptotic normality of weakly dependent random fields, J. Theoret. Probab. 5 (1992), no. 2, 355–373. MR 1157990, 10.1007/BF01046741
  • [3] -, Equivalent mixing conditions for random fields, Technical Report No. 336, Center for Stochastic Processes, Univ. of North Carolina, Chapel Hill, 1990.
  • [4] W. Bryc, Conditional expectation with respect to dependent 𝜎-fields, Proceedings of the seventh conference on probability theory (Braşov, 1982) VNU Sci. Press, Utrecht, 1985, pp. 409–411. MR 867452
  • [5] Raymond Cheng, On the rate of strong mixing in stationary Gaussian random fields, Studia Math. 101 (1992), no. 2, 183–191. MR 1149571
  • [6] Jean-Dominique Deuschel and Daniel W. Stroock, Large deviations, Pure and Applied Mathematics, vol. 137, Academic Press, Inc., Boston, MA, 1989. MR 997938
  • [7] William Feller, An introduction to probability theory and its applications. Vol. II, John Wiley & Sons, Inc., New York-London-Sydney, 1966. MR 0210154
  • [8] F. Móricz, Moment inequalities for the maximum of partial sums of random fields, Acta Sci. Math. (Szeged) 39 (1977), no. 3-4, 353–366. MR 0458535
  • [9] Magda Peligrad, The 𝑟-quick version of the strong law for stationary 𝜙-mixing sequences, Almost everywhere convergence (Columbus, OH, 1988) Academic Press, Boston, MA, 1989, pp. 335–348. MR 1035254
  • [10] Marcel Riesz, Sur les maxima des formes bilinéaires et sur les fonctionnelles linéaires, Acta Math. 49 (1927), no. 3-4, 465–497 (French). MR 1555250, 10.1007/BF02564121
  • [11] William F. Stout, On convergence of 𝜑-mixing sequences of random variables, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 31 (1974/75), 69–70. MR 0358941
  • [12] P. J. Szabłowski, Generalized laws of large numbers and auxiliary results concerning stochastic approximation with dependent disturbances. II, Comput. Math. Appl. 13 (1987), no. 12, 973–987. MR 898944, 10.1016/0898-1221(87)90068-X

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Keywords: Maximal correlation, almost surely convergent series, strong law of large numbers
Article copyright: © Copyright 1993 American Mathematical Society