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Two Hypotheses on the Exponential Class in the Class Of O-subexponential Infinitely Divisible Distributions

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  • Toshiro Watanabe

    (The University of Aizu)

Abstract

Two hypotheses on the class $${\mathcal {L}}(\gamma )$$ L ( γ ) in the class $$\mathcal {OS}\cap \mathcal {ID}$$ OS ∩ ID are discussed. Two weak hypotheses on the class $${\mathcal {L}}(\gamma )$$ L ( γ ) in the class $$\mathcal {OS}\cap \mathcal {ID}$$ OS ∩ ID are proved. A necessary and sufficient condition in order that, for every $$t>0$$ t > 0 , the t-th convolution power of a distribution in the class $$\mathcal {OS}\cap \mathcal {ID}$$ OS ∩ ID belongs to the class $${\mathcal {L}}(\gamma )$$ L ( γ ) is given. Sufficient conditions are given for the validity of two hypotheses on the class $${\mathcal {L}}(\gamma )$$ L ( γ ) .

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:2:d:10.1007_s10959-019-00976-z
    DOI: 10.1007/s10959-019-00976-z
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    References listed on IDEAS

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    1. Embrechts, Paul & Goldie, Charles M., 1982. "On convolution tails," Stochastic Processes and their Applications, Elsevier, vol. 13(3), pages 263-278, September.
    2. 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.
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