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The Lévy-Itô decomposition in free probability

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  • Department of Mathematical Sciences
In this paper we prove the free analog of the Lévy-Itô decomposition for Lévy processes. A significant part of the proof consists of introducing free Poisson random measures, proving their existence and developing a theory of integration with respect to such measures. The existence of free Poisson random measures also yields, via the free Lévy-Itô decomposition, an alternative proof of the general existence of free Lévy processes (in law).
Original languageEnglish
JournalProb. Theory Rel. Fields
Volume131
Issue2
Pages (from-to)197-228
Number of pages32
DOIs
Publication statusPublished - 2005

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