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On the almost decrease of a subexponential density

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  • Jiang, Tao
  • Wang, Yuebao
  • Cui, Zhaolei
  • Chen, Yuxin

Abstract

In this paper, a subexponential density on R+∪{0} without the almost decrease is constructed. Correspondingly, a similar result is also obtained for the long-tailed density excluding the subexponential density. Additionally, in contrast to the first result, a sufficient condition is provided under which the density is almost decreasing. Some interesting conclusions are presented when the above results are applied to the study of local distribution and infinitely divisible distribution. For example, a substantial difference between the subexponential distribution and the local subexponential distribution is clearly shown.

Suggested Citation

  • Jiang, Tao & Wang, Yuebao & Cui, Zhaolei & Chen, Yuxin, 2019. "On the almost decrease of a subexponential density," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 71-79.
    • Handle: RePEc:eee:stapro:v:153:y:2019:i:c:p:71-79
    DOI: 10.1016/j.spl.2019.05.020
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    References listed on IDEAS

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    1. Asmussen, Søren & Kalashnikov, Vladimir & Konstantinides, Dimitrios & Klüppelberg, Claudia & Tsitsiashvili, Gurami, 2002. "A local limit theorem for random walk maxima with heavy tails," Statistics & Probability Letters, Elsevier, vol. 56(4), pages 399-404, February.
    2. Yang, Yang & Leipus, Remigijus & Siaulys, Jonas, 2010. "Local precise large deviations for sums of random variables with O-regularly varying densities," Statistics & Probability Letters, Elsevier, vol. 80(19-20), pages 1559-1567, October.
    3. 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.
    4. Sgibnev, M. S., 1996. "On the distribution of the maxima of partial sums," Statistics & Probability Letters, Elsevier, vol. 28(3), pages 235-238, July.
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    Cited by:

    1. Zhaolei Cui & Yuebao Wang & Hui Xu, 2022. "Local Closure under Infinitely Divisible Distribution Roots and Esscher Transform," Mathematics, MDPI, vol. 10(21), pages 1-24, November.

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