A new factorization property of the selfdecomposable probability measures.

DOI10.1214/009117904000000225zbMath1046.60002arXivmath/0205316OpenAlexW3103771479MaRDI QIDQ1879827

Bertram M. Schreiber, Aleksander M. Iksanov, Zbigniew J. Jurek

Publication date: 15 September 2004

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0205316

zbMATH Keywords

stableinfinitely divisiblefactorization propertyLévy exponentbackground driving Lévy processLévy spectral measureclass \(L\)\(s\)-selfdecomposableclass \({\mathcal U}\)Lévy stochastic area integralselfdecomposable

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Processes with independent increments; Lévy processes (60G51) Stochastic integrals (60H05) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

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Cites Work

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• Limit distributions and one-parameter groups of linear operators on Banach spaces
• Relations between the \(\epsilon\)-selfdecomposable and selfdecomposable measures
• An alternative approach to multiply self-decomposable probability measures on Banach spaces
• Class L of multivariate distributions and its subclasses
• Generalized gamma convolutions and related classes of distributions and densities
• Infinitely divisible distributions with unimodal Levy spectral functions
• Representation of certain infinitely divisible probability measures on Banach spaces
• Characterization of subclasses of class L probability distributions
• Algebraic properties of beta and gamma distributions, and applications
• Probability in Banach spaces, 9: Proceedings from the 9th international conference on probability in Banach spaces, held at Sandjberg, Denmark, August 16-21, 1993
• On asymptotic errors in discretization of processes
• Self-similar processes with independent increments associated with Lévy and Bessel processes.
• Continuity of Certain Random Integral Mappings and the Uniform Integrability of Infinitely Divisible Measures
• An integral representation for selfdecomposable banach space valued random variables
• Self-decomposable probability measures on Banach spaces
• Brownian motion with quadratic killing and some implications
• Shot Noise Distributions and Selfdecomposability