Open AccessLévy laws in free probability
Author(s) -
Ole E. Barndorff–Nielsen,
Steen Thorbjørnsen
Publication year - 2002
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.232052399
Subject(s) - divisibility rule , bijection , infinite divisibility , probability theory , mathematics , free probability , noncommutative geometry , probability measure , probability distribution , subject (documents) , mathematical economics , discrete mathematics , pure mathematics , statistics , computer science , library science
This article and its sequel outline recent developments in the theory of infinite divisibility and Lévy processes in free probability, a subject area belonging to noncommutative (or quantum) probability. The present paper discusses the classes of infinitely divisible probability measures in classical and free probability, respectively, via a study of the Bercovici-Pata bijection between these classes.