Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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PRECISE ASYMPTOTICS IN STRONG LIMIT THEOREMS FOR NEGATIVELY ASSOCIATED RANDOM FIELDS

  • Ryu, Dae-Hee (Department of Computer Science, ChungWoon University)
  • Received : 2010.01.05
  • Accepted : 2010.03.04
  • Published : 2010.05.30
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Abstract

Let {$X_n$, $n\;{\in}\;\mathbb{Z}_+^d$} be a field of identically distributed and negatively associated random variables with mean zero and set $S_n\;=\;{\sum}_{k{\leq}n}\;X_k$, $n\;{\in}\;\mathbb{Z}_+^d$, $d\;{\geq}\;2$. We investigate precise asymptotics for ${\sum}_n|n|^{r/p-2}P(|S_n|\;{\geq}\;{\epsilon}|n|^{1/p}$ and ${\sum}_n\;\frac{(\log\;|n|)^{\delta}}{|n|}P(|S_n|\;{\geq}\;{\epsilon}\;\sqrt{|n|\log|n|)}$, ($0\;{\leq}\;{\delta}\;{\leq}\;1$) as ${\epsilon}{\searrow}0$.

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References

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