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Lower limits and upper limits for tails of random sums supported on

Author

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  • Yu, Changjun
  • Wang, Yuebao
  • Cui, Zhaolei

Abstract

Based on Rudin (1973), Foss and Korshunov (2007) and Denisov et al. (2008), we study the lower limits and upper limits of the quotients of tails as x-->[infinity], where [tau] is a non-negative integer-valued random variable and F is a distribution supported on . Some of the new results, which are different from the corresponding results of , give a positive answer to Problem 2 of Watanabe (2008) under certain conditions. In addition, we give some corresponding results for the local versions and density versions.

Suggested Citation

  • Yu, Changjun & Wang, Yuebao & Cui, Zhaolei, 2010. "Lower limits and upper limits for tails of random sums supported on," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1111-1120, July.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:13-14:p:1111-1120
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    References listed on IDEAS

    as
    1. Wang, Yuebao & Yang, Yang & Wang, Kaiyong & Cheng, Dongya, 2007. "Some new equivalent conditions on asymptotics and local asymptotics for random sums and their applications," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 256-266, March.
    2. Embrechts, Paul & Goldie, Charles M., 1982. "On convolution tails," Stochastic Processes and their Applications, Elsevier, vol. 13(3), pages 263-278, September.
    3. Yu, Changjun & Wang, Yuebao & Yang, Yang, 2010. "The closure of the convolution equivalent distribution class under convolution roots with applications to random sums," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 462-472, March.
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    Cited by:

    1. Yuebao Wang & Hui Xu & Dongya Cheng & Changjun Yu, 2018. "The local asymptotic estimation for the supremum of a random walk with generalized strong subexponential summands," Statistical Papers, Springer, vol. 59(1), pages 99-126, March.
    2. Toshiro Watanabe, 2022. "Embrechts–Goldie’s Problem on the Class of Lattice Convolution Equivalent Distributions," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2622-2642, December.
    3. Lin, Jianxi & Wang, Yuebao, 2012. "New examples of heavy-tailed O-subexponential distributions and related closure properties," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 427-432.
    4. Wang, Kaiyong & Yang, Yang & Yu, Changjun, 2013. "Estimates for the overshoot of a random walk with negative drift and non-convolution equivalent increments," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1504-1512.

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