On free and classical type \(G\) distributions

DOI10.1214/09-BJPS039zbMath1209.62010OpenAlexW1969395327MaRDI QIDQ985982

Octavio Arizmendi, Victor Perez-Abreu, Ole Eiler Barndorff-Nielsen

Publication date: 9 August 2010

Published in: Brazilian Journal of Probability and Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/09-bjps039

zbMATH Keywords

free infinite divisibilityfree compound Poisson distributionsfree multiplicative convolutionstransformation of Lévy measuresvariance mixtures of Gaussians

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Characteristic functions; other transforms (60E10) Characterization and structure theory of statistical distributions (62E10)

Related Items (6)

\(k\)-divisible random variables in free probability ⋮ A class of multivariate infinitely divisible distributions related to arcsine density ⋮ Free infinite divisibility of free multiplicative mixtures of the Wigner distribution ⋮ On a class of explicit Cauchy-Stieltjes transforms related to monotone stable and free Poisson laws ⋮ Selfdecomposable fields ⋮ On the class of distributions of subordinated Lévy processes and bases

Cites Work

• Some classes of multivariate infinitely divisible distributions admitting stochastic integral representations
• A note on new classes of infinitely divisible distributions on \(\mathbb{R}^{d}\)
• Stable laws and domains of attraction in free probability theory
• Multiplication of free random variables and the \(S\)-transform: the case of vanishing mean
• Regularizing mappings of Lévy measures
• Additive processes and stochastic integrals
• The $S$-transform of symmetric probability measures with unbounded supports
• Lectures on the Combinatorics of Free Probability
• Matrix Subordinators and Related Upsilon Transformations
• A CONNECTION BETWEEN FREE AND CLASSICAL INFINITE DIVISIBILITY
• Exercises in Probability
• Infinite Divisibility and Variance Mixtures of the Normal Distribution
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