Representations of Urbanik's classes and multiparameter Ornstein-Uhlenbeck processes

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    Abstract

    A class of integrals with respect to homogeneous Lévy bases on Rk is considered. In the one-dimensional case k=1 this class corresponds to the selfdecomposable distributions. Necessary and sufficient conditions for existence as well as some representations of the integrals are given. Generalizing the one-dimensional case it is shown that the class of integrals corresponds to Urbanik's class Lk-1(R). Finally, multiparameter Ornstein-Uhlenbeck processes are defined and studied.
    Original languageEnglish
    JournalElectronic Communications in Probability
    Volume16
    Pages (from-to)200-212
    Number of pages13
    ISSN1083-589X
    Publication statusPublished - 2011

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