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Asymptotic lower bounds of precise large deviations with nonnegative and dependent random variables

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  • He, Wei
  • Cheng, Dongya
  • Wang, Yuebao
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    Abstract

    In this paper, asymptotic lower bounds of precise large deviations for non-random sums and random sums of nonnegative random variables (r.v.s) are derived under some fairly weak conditions. The obtained results are used to derive asymptotic lower bounds of precise large deviations in a multi-risk model. All the results we establish extend and improve the related existing results substantially.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167715212003653
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 83 (2013)
    Issue (Month): 1 ()
    Pages: 331-338

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    Handle: RePEc:eee:stapro:v:83:y:2013:i:1:p:331-338

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    Related research

    Keywords: Precise large deviations; Asymptotic lower bound; Non-random sums; Random sums; Dependence structure;

    References

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    1. Liu, Li, 2009. "Precise large deviations for dependent random variables with heavy tails," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1290-1298, May.
    2. 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.
    3. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
    4. Liu, Xijun & Gao, Qingwu & Wang, Yuebao, 2012. "A note on a dependent risk model with constant interest rate," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 707-712.
    5. 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.
    6. Lu, Dawei, 2012. "Lower bounds of large deviation for sums of long-tailed claims in a multi-risk model," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1242-1250.
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