An integral representation for selfdecomposable banach space valued random variables

DOI10.1007/BF00538800zbMath0488.60028MaRDI QIDQ3949723

Zbigniew J. Jurek, Wim Vervaat

Publication date: 1983

Published in: Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete (Search for Journal in Brave)

zbMATH Keywords

stationary independent incrementsselfdecomposablerepresentations of characteristic functional

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07)

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Cites Work

• Unnamed Item
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• Limit distributions and one-parameter groups of linear operators on Banach spaces
• Class L of multivariate distributions and its subclasses
• Exponential moments of vector valued random series and triangular arrays
• On a continuous analogue of the stochastic difference equation \(X_ n\) = rho X//(n-1) + \(B_ n\).
• Type, cotype and Levy measures in Banach spaces
• Representation of certain infinitely divisible probability measures on Banach spaces
• Characterization of subclasses of class L probability distributions
• On the convergence of sums of independent Banach space valued random variables
• On the Continuity of the Distribution of a Sum of Dependent Variables Connected with Independent Walks on Lines
• Lois e(?) dans les espaces vectoriels et lois stables
• Remarks on stable measures on Banach spaces
• Lévy's probability measures on Banach spaces
• Self-decomposable probability measures on Banach spaces
• Isomorphic characterizations of inner product spaces by orthogonal series with vector valued coefficients
• Weak convergence of probability measures and random functions in the function space D[0,∞)