Urbanik type subclasses of free-infinitely~divisible~transforms

• Autorzy: Jurek Zbigniew J.

Identyfikatory

DOI

0.37190/0208-4147.00010

• Języki publikacji: EN

Abstrakty

EN

For the class of free-infinitely divisible transforms we introduce three families of increasing Urbanik type subclasses. They begin with the class of free-normal transforms and end up with the whole class of free- infinitely divisible transforms. Those subclasses are derived from the ones of classical infinitely divisible measures for which random integral repre- sentations are known. Special functions like Hurwitz–Lerch, polygamma and hypergeometric functions appear in kernels of the corresponding integral representations.

Słowa kluczowe

EN

characteristic function; infinite divisibility; selfdecomposability; s-selfdecomposability; Lévy-Khinchin formula; free-infinite divisibility; Nevanlinna-Pick functions; polygamma function; hypergeometric function

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2022
• Tom: Vol. 42, Fasc. 1
• Strony: 23--39
• Opis fizyczny: Bibliogr. 26 poz.

Twórcy

autor

Jurek Zbigniew J.

• Institute of Mathematics, Wroclaw University, Pl. Grunwaldzki 2/4, 50-384 Wroclaw, Poland

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