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The general principle for precise large deviations of heavy-tailed random sums

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  • Lin, Jianxi

Abstract

Let {Xn;n[greater-or-equal, slanted]1} be an arbitrary sequence of heavy-tailed random variables, independent of a process of nonnegative, integer-valued rv's {N(t);t[greater-or-equal, slanted]0}. In this paper, we present a necessary and a sufficient condition on {N(t);t[greater-or-equal, slanted]0} under which the precise large deviation result for nonrandom sum can be extended to the random sum SN(t). The results we obtain not only generalize but also improve some related classical ones.

Suggested Citation

  • Lin, Jianxi, 2008. "The general principle for precise large deviations of heavy-tailed random sums," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 749-758, April.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:6:p:749-758
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    References listed on IDEAS

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    1. Aleksandras Baltrūnas & Claudia Klüppelberg, 2004. "Subexponential Distributions - Large Deviations with Applications to Insurance and Queueing Models," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 46(1), pages 145-154, March.
    2. 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.
    3. Matula, Przemyslaw, 1992. "A note on the almost sure convergence of sums of negatively dependent random variables," Statistics & Probability Letters, Elsevier, vol. 15(3), pages 209-213, October.
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    Cited by:

    1. Yiqing Chen & Kam C. Yuen & Kai W. Ng, 2011. "Precise Large Deviations of Random Sums in Presence of Negative Dependence and Consistent Variation," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 821-833, December.
    2. He, Wei & Cheng, Dongya & Wang, Yuebao, 2013. "Asymptotic lower bounds of precise large deviations with nonnegative and dependent random variables," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 331-338.
    3. Chen, Yiqing & Yuen, Kam C., 2012. "Precise large deviations of aggregate claims in a size-dependent renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 457-461.

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