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

  • Yiqing Chen (a1), Anyue Chen (a2) and Kai W. Ng (a3)
Abstract

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.

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Copyright
Corresponding author
Postal address: Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 7ZL, UK.
∗∗ Email address: yiqing.chen@liv.ac.uk
∗∗∗ Postal address: Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong.
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  • ISSN: 0021-9002
  • EISSN: 1475-6072
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