On the class of infinitely divisible distributions and on its subclasses
L. Kubik (1966)
Studia Mathematica
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L. Kubik (1966)
Studia Mathematica
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Zbigniew Jurek (1979)
Banach Center Publications
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Wei-Bin Zeng (1992)
Stochastica
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In this note we give an elementary proof of a characterization for stability of multivariate distributions by considering a functional equation.
Grażyna Mazurkiewicz (2010)
Banach Center Publications
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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).
Kłosowska, Maria (2015-10-26T10:02:45Z)
Acta Universitatis Lodziensis. Folia Mathematica
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Artikis, Theodore (1983-1984)
Portugaliae mathematica
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Theodore Artikis (1983)
Archivum Mathematicum
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Zbigniew J. Jurek
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CONTENTSIntroduction....................................................................................................................................................................... 5Chapter I. Distributions of sums or infinitesimal random variables § 1. Notations, definitions and preliminary facts.......................................................................................... 6 § 2. Existence of limit distributions for sums of infinitesimal random variables..............................................
L. J. Savage (1969)
Applicationes Mathematicae
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M. Kłosowska (1972)
Studia Mathematica
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L. Kubik (1962)
Studia Mathematica
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