The Lévy-Itô decomposition in free probability

Ole Eiler Barndorff-Nielsen, Steen Thorbjørnsen

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    Abstract

    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).
    OriginalsprogEngelsk
    TidsskriftProb. Theory Rel. Fields
    Vol/bind131
    Nummer2
    Sider (fra-til)197-228
    Antal sider32
    DOI
    StatusUdgivet - 2005

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