On the infinite divisibility of scale mixtures of symmetric α-stable distributions, α ∈ (0,1]

• Autorzy: Grażyna Mazurkiewicz
• Języki publikacji: EN

Abstrakty

EN

The paper contains a new and elementary proof of the fact that if α ∈ (0,1] then every scale mixture of a symmetric α-stable probability measure is infinitely divisible. This property is known to be a consequence of Kelker's result for the Cauchy distribution and some nontrivial properties of completely monotone functions. It is known that this property does not hold for α = 2. The problem discussed in the paper is still open for α ∈ (1,2).

Kategorie tematyczne

• 60E10: Characteristic functions; other transforms
• 60B05: Probability measures on topological spaces
• 60A10: Probabilistic measure theory
• 60E05: Distributions: general theory
• 60E07: Infinitely divisible distributions; stable distributions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2010
• Tom: 90
• Numer: 1
• Strony: 79-82

Daty

wydano

2010

Twórcy

autor

Grażyna Mazurkiewicz

• Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Szafrana 4a, 65-516 Zielona Góra, Poland

Identyfikatory

DOI

10.4064/bc90-0-5