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  • The Strong Law of Large Numbers for Extended Negatively Dependent Random Variables

  • Part of
  • Yiqing Chen, Anyue Chen, Kai W. Ng
  • Journal:
    Journal of Applied Probability / Volume 47 / Issue 4 / December 2010
    Published online by Cambridge University Press:
    14 July 2016, pp. 908-922
    Print publication:
    December 2010
    • Article
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  • A sequence of random variables is said to be extended negatively dependent (END) if the tails of its finite-dimensional distributions in the lower-left and upper-right corners are dominated by a multiple of the tails of the corresponding finite-dimensional distributions of a sequence of independent random variables with the same marginal distributions. The goal of this paper is to establish the strong law of large numbers for a sequence of END and identically distributed random variables. In doing so we derive some new inequalities of large deviation type for the sums of END and identically distributed random variables being suitably truncated. We also show applications of our main result to risk theory and renewal theory.