On stable distributions in Hilbert space
R. Jajte (1968)
Studia Mathematica
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R. Jajte (1968)
Studia Mathematica
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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 (1974)
Colloquium Mathematicae
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M. Kłosowska (1977)
Colloquium Mathematicae
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J. Barańska (1973)
Colloquium Mathematicae
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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).
Zbigniew Jurek (1979)
Banach Center Publications
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A. Kumar, V. Mandrekar (1972)
Studia Mathematica
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Adrienne W. Kemp (1978)
Applicationes Mathematicae
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Fernand Pelletier, Rebhia Saffidine (2013)
Annales de la faculté des sciences de Toulouse Mathématiques
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The purpose of this paper is to give an illustration of results on integrability of distributions and orbits of vector fields on Banach manifolds obtained in [5] and [4]. Using arguments and results of these papers, in the context of a separable Hilbert space, we give a generalization of a Theorem of accessibility contained in [3] and [6] for articulated arms and snakes in a finite dimensional Hilbert space.
L. Kubik (1966)
Studia Mathematica
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R. Jajte (1968)
Colloquium Mathematicae
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W. Krakowiak (1980)
Colloquium Mathematicae
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M. Kłosowska (1973)
Colloquium Mathematicae
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