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Precise large deviations for randomly weighted sums of negatively dependent random variables with consistently varying tails. (English) Zbl 1154.60316

Summary: Let \(\{X_k,k\geq 1\}\) be a sequence of negatively dependent random variables with common distribution \(F\) and mean 0. Suppose that \(\widetilde F(x)=1-F(x)\) is positive for all \(x\) and consistently varying as \(x\to\infty\). Let \(\{\theta_k,\;k\geq 1\}\) be another sequence of random variables independent of \(\{X_k,\;k\geq 1\}\) satisfying \(P(a\leq\theta_k\leq b)=1\) for some \(0<a\leq b<\infty\), \(k\geq 1\). The paper investigates large deviations for the randomly weighted sums.

MSC:

60F10 Large deviations
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