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Precise large deviations for dependent random variables with heavy tails

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  • Liu, Li

Abstract

By extending the negatively dependent (ND) structure, the paper puts forth the concept of extended negative dependence (END). The results show that the END structure has no effect on the asymptotic behavior of precise large deviations of partial sums and random sums for non-identically distributed random variables on (-[infinity],+[infinity]).

Suggested Citation

  • Liu, Li, 2009. "Precise large deviations for dependent random variables with heavy tails," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1290-1298, May.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:9:p:1290-1298
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    References listed on IDEAS

    as
    1. Rob Kaas & Qihe Tang, 2003. "Note on the Tail Behavior of Random Walk Maxima with Heavy Tails and Negative Drift," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(3), pages 57-61.
    2. Cline, D. B. H. & Samorodnitsky, G., 1994. "Subexponentiality of the product of independent random variables," Stochastic Processes and their Applications, Elsevier, vol. 49(1), pages 75-98, January.
    3. Schlegel, Sabine, 1998. "Ruin probabilities in perturbed risk models," Insurance: Mathematics and Economics, Elsevier, vol. 22(1), pages 93-104, May.
    4. Wang, Dingcheng & Tang, Qihe, 2004. "Maxima of sums and random sums for negatively associated random variables with heavy tails," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 287-295, July.
    5. Tang, Qihe & Tsitsiashvili, Gurami, 2003. "Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks," Stochastic Processes and their Applications, Elsevier, vol. 108(2), pages 299-325, December.
    6. Tang, Qihe & Su, Chun & Jiang, Tao & Zhang, Jinsong, 2001. "Large deviations for heavy-tailed random sums in compound renewal model," Statistics & Probability Letters, Elsevier, vol. 52(1), pages 91-100, March.
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