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

Toshiro Watanabe ()
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Toshiro Watanabe: The University of Aizu

Journal of Theoretical Probability, 2021, vol. 34, issue 2, 852-873

Abstract: 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 ) .

Keywords: Exponential class; O-subexponentiality; Infinite divisibility; Convolution roots; 60E07; 60G51 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10959-019-00976-z

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