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Weak laws of large numbers for arrays under a condition of uniform integrability

Andrei Volodin|성수학|Supranee Lisawadi
대한수학회 (The Korean Mathematical Society)|2008.01|대한수학회지 (Journal of the KMS)|제45권 제1호|pp. 289-300

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참고문헌

키워드

weak law of large numbersnegative associationconvergence in probabilityuniform integrabilityr-mean convergencemartingale difference sequencenegative dependence.
주제분류수학

초록

For an array of dependent random variables satisfying a new notion of uniform integrability, weak laws of large numbers are obtained. Our results extend and sharpen the known results in the literature.

Abstract

For an array of dependent random variables satisfying a new notion of uniform integrability, weak laws of large numbers are obtained. Our results extend and sharpen the known results in the literature.

참고문헌 (14)

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  3. N. Etemadi, "An elementary proof of the strong law of large numbers", Zeitschrift für Wahrscheinlichkeitstheorie verw Gebiete, 55(1), pp.119~122 (1981)
  4. A. Gut, "The weak law of large numbers for arrays", Statistics & Probability Letters, 14(1), pp.49~52 (1992)
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  7. V. Kruglov, "Growth of sums of pairwise-independent random variables with infinite means", Teoriya Veroyatnostei ee Primeneniya, 51(2), pp.382~385 (2006)
  8. D. Landers, "Laws of large numbers for pairwise independent uniformly integrable random variables", Mathematische Nachrichten, 130, pp.189~192 (1987)
  9. D. Li, "On the strong law of large numbers for sequences of pairwise negative quadrant dependent random variables", BULLETIN of the Institute of Mathematics. Academia Sinica (N.S.), 1(2), pp.281~305 (2006)
  10. M. Ord´onez Cabrera, "Convergence of weighted sums of random variables and uniform integrability concerning the weights", Collectanea Mathematica, 45(2), pp.121~132 (1994)
  11. M. Ord´onez Cabrera, "Mean convergence theorems and weak laws of large numbers for weighted sums of random variables under a condition of weighted integrability", Journal of Mathematical Analysis and Applications, 305(2), pp.644~658 (2005)
  12. Q. M. Shao, "A comparison theorem on moment inequalities between negatively associated and independent random variables", Journal of Theoretical Probability, 13(2), pp.343~356 (2000)
  13. S. H. Sung, "Weak law of large numbers for arrays of random variables", Statistics & Probability Letters, 42(3), pp.293~298 (1999)
  14. S. H. Sung, "On the weak laws for arrays of random variables", Statistics & Probability Letters, 72(4), pp.291~298 (2005)

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