대한수학회지 (Journal of the Korean Mathematical Society)

  • 제53권1호
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  • Pages.45-55
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  • 2016
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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ON THE STRONG LAW OF LARGE NUMBERS FOR WEIGHTED SUMS OF NEGATIVELY SUPERADDITIVE DEPENDENT RANDOM VARIABLES

  • SHEN, AITING (SCHOOL OF MATHEMATICAL SCIENCES ANHUI UNIVERSITY)
  • 투고 : 2014.04.14
  • 발행 : 2016.01.01
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초록

Let {$X_n,n{\geq}1$} be a sequence of negatively superadditive dependent random variables. In the paper, we study the strong law of large numbers for general weighted sums ${\frac{1}{g(n)}}{\sum_{i=1}^{n}}{\frac{X_i}{h(i)}}$ of negatively superadditive dependent random variables with non-identical distribution. Some sufficient conditions for the strong law of large numbers are provided. As applications, the Kolmogorov strong law of large numbers and Marcinkiewicz-Zygmund strong law of large numbers for negatively superadditive dependent random variables are obtained. Our results generalize the corresponding ones for independent random variables and negatively associated random variables.

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과제정보

연구 과제 주관 기관 : National Natural Science Foundation of China

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