Large deviations in spaces of stable type
Evarist Giné (1983)
Annales de l'I.H.P. Probabilités et statistiques
Similarity:
Evarist Giné (1983)
Annales de l'I.H.P. Probabilités et statistiques
Similarity:
Grażyna Mazurkiewicz (2005)
Discussiones Mathematicae Probability and Statistics
Similarity:
In this paper, we study some analytical properties of the symmetric α-stable density function.
Evarist Giné (1979)
Séminaire de probabilités de Strasbourg
Similarity:
Grażyna Mazurkiewicz (2010)
Banach Center Publications
Similarity:
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).
W. Krakowiak (1979)
Colloquium Mathematicae
Similarity:
Joel Zinn (1976)
Studia Mathematica
Similarity:
J. Kuelbs, V. Mandrekar (1974)
Studia Mathematica
Similarity:
Marchal, Philippe (2005)
Electronic Communications in Probability [electronic only]
Similarity:
Marta Borowiecka-Olszewska, Jolanta K. Misiewicz (2003)
Discussiones Mathematicae Probability and Statistics
Similarity:
In this paper, we consider a symmetric α-stable p-sub-stable two-dimensional random vector. Our purpose is to show when the function is a characteristic function of such a vector for some p and α. The solution of this problem we can find in [3], in the language of isometric embeddings of Banach spaces. Our proof is based on simple properties of stable distributions and some characterization given in [4].
J. Bastero Eleizalde, J. M. Mira Ros (1987)
Extracta Mathematicae
Similarity:
J. Bastero, Y. Raynaud (1989)
Studia Mathematica
Similarity: