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Weak Laws for Weighted Sums of Random Variables

성수학
대한수학회 (The Korean Mathematical Society)|2004.05|대한수학회보 (Bulletin of the KMS)|제41권 제2호|pp. 275-282

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Abstract

Let {a_{ni}, u_nle ile v_n, nge 1} be an array ofconstants. Let {X_{ni}, u_nle ile v_n, nge 1} be{a_{ni}}-uniformly integrable random variables. Weak laws forthe weighted sums sum_{i=u_n}^{v_n} a_{ni}X_{ni} are obtained.

참고문헌 (10)

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  3. "paper A general weak law of large numbers for arrays", 24, pp.205~209 (1996)
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  5. "Ordonez Cabrera \paper Convergence of weighted sums of random variables and uniform integrability concerning the weights \jour Collect. Math. \vol 45 \issue 2 \yr 1994 \pages 121--132"
  6. "E. Pruitt \paper Summability of independent random variables \jour J. Math. Mech. \vol 15 \yr 1966 \pages 769--776"
  7. "K. Rohatgi \paper Convergence of weighted sums of independent random variables \jour Proc. Cambridge Philos. Soc. \vol 69 \yr 1971 \pages 305--307"
  8. "paper Weak law of large numbers for arrays", 38, pp.101~105 (1998)
  9. "Weak law of large numbers for arrays ofrandom variables", 42, pp.293~298 (1999)
  10. "C. Wang and M. B. Rao \paper A note onconvergence of weighted sums of random variables \jour Internat. J. Math. Math. Sci. \vol 8 \issue 4 \yr 1985 \pages805--812"

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