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Large deviations for dependent heavy tailed random variables. (English) Zbl 1296.60070

Summary: Let \(\{X_{n},n\geq1\}\) be a stationary sequence of random variables with heavy tails. In this paper, we study the logarithmic asymptotic behaviors for the distributions of the partial sums \(S_n=\sum_{i=1}^{n}X_i\) under the assumption that \(\{X_{n},n\geq1\}\) is a sequence of dependent random variables. Our main interest is in the crude estimates \(P(|S_{n}|>n^{x})\approx n^{-\alpha x+1}\) for appropriate values \(x\) where \(\alpha\) is a specific parameter. Some results in this paper extend the works of Y. Hu and H. Nyrhinen [J. Theor. Probab. 17, No. 3, 761–768 (2004; Zbl 1068.60038)].

MSC:

60F10 Large deviations

Citations:

Zbl 1068.60038
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References:

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