Asymptotic behaviors of convolution powers of the Riemann zeta distribution

In probability theory, there are discrete and continuous distributions. Generally speaking, we do not have sufficient kinds and properties of discrete ones compared to the continuous ones. In this paper, we treat the Riemann zeta distribution as a representative of few known discrete distributions w...

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Bibliographic Details
Published in:Lithuanian mathematical journal 2023, Vol.63 (1), p.1-12
Main Authors: Aoyama, Takahiro, Namba, Ryuya, Ota, Koki
Format: Article
Language:English
Subjects:
Actuarial Sciences
Asymptotic properties
Convolution
Mathematics
Mathematics and Statistics
Number Theory
Ordinary Differential Equations
Probability theory
Probability Theory and Stochastic Processes
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Summary:In probability theory, there are discrete and continuous distributions. Generally speaking, we do not have sufficient kinds and properties of discrete ones compared to the continuous ones. In this paper, we treat the Riemann zeta distribution as a representative of few known discrete distributions with infinite supports. We discuss some asymptotic behaviors of convolution powers of the Riemann zeta distribution.
ISSN:0363-1672
1573-8825
DOI:10.1007/s10986-023-09585-0