On the Self-Decomposability of Euler's Gamma Function |
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| Authors: | Grigelionis B |
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| Institution: | (1) Institute of Mathematics and Informatics, Akademijos 4, LT-2021 Vilnius;(2) Vilnius University, Naugarduko 24, LT-2600 Vilnius, Lithuania |
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| Abstract: | Let  be Euler's Gamma function. We prove that, for all   0,  > 0,  > 0,  > 0, the function (( + iz)/()
i
z)
, z  R
1, is a self-decomposable characteristic function from the Thorin class
and derive its explicit canonical form. Similarly to 1], we also describe several classes of Lévy-type stochastic processes related to . |
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| Keywords: | Euler's Gamma function Gamma distribution Gumbel distribution self-decomposability self-similarity Lé vy process Ornstein– Uhlenbeck-type process Esscher transform mixed exponential process |
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