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Strong limit theorems for weighted sums of NOD sequence and exponential inequalities

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Some properties for negatively orthant dependent sequence are discussed. Some strong limit results for the weighted sums are obtained, which generalize the corresponding results for independent sequence and negatively associated sequence. At last, exponential inequalities for negatively orthant dependent sequence are presented.

Abstract

Some properties for negatively orthant dependent sequence are discussed. Some strong limit results for the weighted sums are obtained, which generalize the corresponding results for independent sequence and negatively associated sequence. At last, exponential inequalities for negatively orthant dependent sequence are presented.

참고문헌 (11)

  1. A. Adler, "On the nonexistence of a law of the iterated logarithm for weighted sums of identically distributed random variables", J. Appl. Math. Stochastic Anal, 3(2), pp.135~140 (1990)
  2. R. G. Antonini, "On the strong convergence of weighted sums", Stochastic Anal. Appl, 19(6), pp.903~909 (2001)
  3. A. Bozorgnia, "Limit theorems for dependent random variables", World Congress of Nonlinear Analysts '92, 통권 : I-IV, pp.1639~1650 (1992)
  4. Y. S. Chow, "Limiting behavior of weighted sums of independent random variables", Ann. Probability, 1(5), pp.810~824 (1973)
  5. V. Fakoor, "Probability inequalities for sums of negatively dependent random variables", Pakistan J. Statist, 21(3), pp.257~264 (2005)
  6. K. Joag-Dev, "Negative association of random variables with applica- tions", Ann. Statist, 11(1), pp.286~295 (1983)
  7. H. C. Kim, "The Hajek-Renyi inequality for weighted sums of negatively orthant depen- dent random variables", Int. J. Contemp. Math. Sci, 1(5), pp.297~303 (2006)
  8. 고미화, "Strong laws of large numbers for weighted sums of negatively dependent random variables", 대한수학회지, 43(6), pp.1325~1338 (2006), 대한수학회
  9. 고미화, "Almost sure convergence for weighted sums of negatively orthant dependent random variables", 대한수학회지, 42(5), pp.949~957 (2005), 대한수학회
  10. Q. Wu, "Complete convergence for negatively dependent sequences of random variables", J. Inequal. Appl, pp.10~ (2010)
  11. W. Wu, "On the strong convergence of a weighted sum", Statist. Probab. Lett, 44(1), pp.19~22 (1999)

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