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

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  • Institut for Matematiske Fag
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.
TidsskriftElectronic Communications in Probability
Sider (fra-til)200-212
Antal sider13
StatusUdgivet - 2011

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