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MOMENT CONVERGENCE RATES OF LIL FOR NEGATIVELY ASSOCIATED SEQUENCES

Ke-Ang Fu|Li-Hua Hu
대한수학회 (The Korean Mathematical Society)|2010.03|대한수학회지 (Journal of the KMS)|제47권 제2호|pp. 263-275

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참고문헌

키워드

negative associationChung-type law of the iterated logarithmmoment convergence ratesthe law of the iterated logarithm
주제분류수학

초록

Let {Xn; n ≥ 1} be a strictly stationary sequence of negatively associated random variables with mean zero and finite variance.[수식]We prove that for any[수식]then[수식]and for any b > −1/2[수식]where ¡(·) is the Gamma function and N stands for the standard normal random variable.

Abstract

Let {Xn; n ≥ 1} be a strictly stationary sequence of negatively associated random variables with mean zero and finite variance.[수식]We prove that for any[수식]then[수식]and for any b > −1/2[수식]where ¡(·) is the Gamma function and N stands for the standard normal random variable.

참고문헌 (11)

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  2. P. Billingsley, "Convergence of Probability Measures" (1968), John Wiley & Sons, Inc.
  3. Y. S. Chow, "On the rate of moment convergence of sample sums and extremes", Bull. Inst. Math. Acad. Sinica, 16(3), pp.177~201 (1988)
  4. A. Gut, "Precise asymptotics in the law of the iterated logarithm", Ann. Probab., 28(4), pp.1870~1883 (2000)
  5. Y. Jiang, "Precise rates in the law of iterated logarithm for the moment of i.i.d. random variables", Acta Math. Sin. (Engl. Ser.), 22(3), pp.781~792 (2006)
  6. K. Joag-Dev, "Negative association of random variables, with applications", Ann. Statist., 11(1), pp.286~295 (1983)
  7. Y. X. Li, "Precise asymptotics in complete moment convergence of moving-average processes", Statist. Probab. Lett., 76(13), pp.1305~1315 (2006)
  8. Q. M. Shao, "A comparison theorem on moment inequalities between negatively associated and independent random variables", J. Theoret. Probab., 13(2), pp.343~356 (2000)
  9. Q. M. Shao, "The law of the iterated logarithm for negatively associated random variables", Stochastic Process. Appl., 83(1), pp.139~148 (1999)
  10. W. F. Stout, "Almost Sure Convergence" (1995), Academic
  11. C. Su, "The moment inequalities and weak convergence for negatively associated sequences", Sci. China Ser. A, 40(2), pp.172~182 (1997)

관련 논문AI추천

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