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

Two hypotheses on the class L ( γ ) in the class OS ∩ ID are discussed. Two weak hypotheses on the class L ( γ ) in the class OS ∩ ID are proved. A necessary and sufficient condition in order that, for every t > 0 , the t -th convolution power of a distribution in the class OS ∩ ID belongs to the...

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Bibliographic Details
Published in:Journal of theoretical probability 2021-06, Vol.34 (2), p.852-873
Main Author: Watanabe, Toshiro
Format: Article
Language:English
Subjects:
Convolution
Electric power distribution
Hypotheses
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Statistics
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Summary:Two hypotheses on the class L ( γ ) in the class OS ∩ ID are discussed. Two weak hypotheses on the class L ( γ ) in the class OS ∩ ID are proved. A necessary and sufficient condition in order that, for every t > 0 , the t -th convolution power of a distribution in the class OS ∩ ID belongs to the class L ( γ ) is given. Sufficient conditions are given for the validity of two hypotheses on the class L ( γ ) .
ISSN:0894-9840
1572-9230
DOI:10.1007/s10959-019-00976-z