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Second-Order Behaviour for Self-Decomposable Distributions with Two-Sided Regularly Varying Densities

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  • Toshiro Watanabe

    (The University of Aizu)

Abstract

We investigate the asymptotic behaviour of the difference between the tails of a self-decomposable distribution with a two-sided regularly varying density on the real line and its Lévy measure. Moreover, we study the second-order asymptotic behaviour of the tail of the t-th convolution power of a self-decomposable distribution with a two-sided regularly varying density.

Suggested Citation

  • Toshiro Watanabe, 2022. "Second-Order Behaviour for Self-Decomposable Distributions with Two-Sided Regularly Varying Densities," Journal of Theoretical Probability, Springer, vol. 35(2), pages 1343-1366, June.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:2:d:10.1007_s10959-021-01083-8
    DOI: 10.1007/s10959-021-01083-8
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    References listed on IDEAS

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    1. Lennart Bondesson, 2002. "On the Lévy Measure of the Lognormal and the LogCauchy Distributions," Methodology and Computing in Applied Probability, Springer, vol. 4(3), pages 243-256, September.
    2. 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.
    3. Geluk, J. L., 1992. "Second order tail behaviour of a subordinated probability distribution," Stochastic Processes and their Applications, Elsevier, vol. 40(2), pages 325-337, March.
    4. Jianxi Lin, 2012. "Second order Subexponential Distributions with Finite Mean and Their Applications to Subordinated Distributions," Journal of Theoretical Probability, Springer, vol. 25(3), pages 834-853, September.
    5. Toshiro Watanabe & Kouji Yamamuro, 2010. "Local Subexponentiality and Self-decomposability," Journal of Theoretical Probability, Springer, vol. 23(4), pages 1039-1067, December.
    6. Omey, E. & Willekens, E., 1986. "Second order behaviour of the tail of a subordinated probability distribution," Stochastic Processes and their Applications, Elsevier, vol. 21(2), pages 339-353, February.
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