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Two Non-closure Properties on the Class of Subexponential Densities

Author

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  • Toshiro Watanabe

    (The University of Aizu)

  • Kouji Yamamuro

    (Gifu University)

Abstract

Relations between subexponential densities and locally subexponential distributions are discussed. It is shown that the class of subexponential densities is neither closed under convolution roots nor closed under asymptotic equivalence. A remark is given on the closure under convolution roots for the class of convolution equivalent distributions.

Suggested Citation

  • Toshiro Watanabe & Kouji Yamamuro, 2017. "Two Non-closure Properties on the Class of Subexponential Densities," Journal of Theoretical Probability, Springer, vol. 30(3), pages 1059-1075, September.
    • Handle: RePEc:spr:jotpro:v:30:y:2017:i:3:d:10.1007_s10959-016-0672-x
    DOI: 10.1007/s10959-016-0672-x
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    References listed on IDEAS

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    1. Søren Asmussen & Serguei Foss & Dmitry Korshunov, 2003. "Asymptotics for Sums of Random Variables with Local Subexponential Behaviour," Journal of Theoretical Probability, Springer, vol. 16(2), pages 489-518, April.
    2. Embrechts, Paul & Goldie, Charles M., 1982. "On convolution tails," Stochastic Processes and their Applications, Elsevier, vol. 13(3), pages 263-278, September.
    3. Toshiro Watanabe & Kouji Yamamuro, 2010. "Local Subexponentiality and Self-decomposability," Journal of Theoretical Probability, Springer, vol. 23(4), pages 1039-1067, December.
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    Cited by:

    1. Toshiro Watanabe, 2021. "Two Hypotheses on the Exponential Class in the Class Of O-subexponential Infinitely Divisible Distributions," Journal of Theoretical Probability, Springer, vol. 34(2), pages 852-873, June.
    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.

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