The domain of attraction of a non-Gaussian stable distribution in a Hilbert space
M. Kłosowska (1974)
Colloquium Mathematicae
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M. Kłosowska (1974)
Colloquium Mathematicae
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M. Kłosowska (1973)
Colloquium Mathematicae
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R. Jajte (1968)
Studia Mathematica
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R.G. Laha (1991)
Aequationes mathematicae
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Grażyna Mazurkiewicz (2005)
Discussiones Mathematicae Probability and Statistics
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In this paper, we study some analytical properties of the symmetric α-stable density function.
Kłosowska, Maria (2015-10-26T10:02:45Z)
Acta Universitatis Lodziensis. Folia Mathematica
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Elchanan Mossel, Joe Neeman (2015)
Journal of the European Mathematical Society
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We prove that under the Gaussian measure, half-spaces are uniquely the most noise stable sets. We also prove a quantitative version of uniqueness, showing that a set which is almost optimally noise stable must be close to a half-space. This extends a theorem of Borell, who proved the same result but without uniqueness, and it also answers a question of Ledoux, who asked whether it was possible to prove Borell’s theorem using a direct semigroup argument. Our quantitative uniqueness result...
J. Kuelbs, V. Mandrekar (1974)
Studia Mathematica
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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).
Bogdan Mincer, Kazimierz Urbanik (1979)
Colloquium Mathematicum
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J. Barańska (1973)
Colloquium Mathematicae
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Soltani, A.R., Tarami, B. (2001)
Georgian Mathematical Journal
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Ryznar, Michał, Żak, Tomasz (1998)
Electronic Communications in Probability [electronic only]
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Renze, John, Wagon, Stan, Wick, Brian (2001)
Experimental Mathematics
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Wiesław Cupała (2002)
Discussiones Mathematicae Probability and Statistics
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The Varopoulos-Hardy-Littlewood theory and the spectral analysis are used to estimate the tail of the distribution of the first exit time of α-stable processes.
R.G. Laha (1990)
Aequationes mathematicae
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L. J. Savage (1969)
Applicationes Mathematicae
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