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2011 Representations of Urbanik's classes and multiparameter Ornstein-Uhlenbeck processes
Svend-Erik Graversen, Jan Pedersen
Author Affiliations +
Electron. Commun. Probab. 16: 200-212 (2011). DOI: 10.1214/ECP.v16-1621

Abstract

A class of integrals with respect to homogeneous Lévy bases on $\mathbb{R}^k$ 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 $ L_{k-1}(R)$. Finally, multiparameter Ornstein-Uhlenbeck processes are defined and studied.

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Svend-Erik Graversen. Jan Pedersen. "Representations of Urbanik's classes and multiparameter Ornstein-Uhlenbeck processes." Electron. Commun. Probab. 16 200 - 212, 2011. https://doi.org/10.1214/ECP.v16-1621

Information

Accepted: 18 April 2011; Published: 2011
First available in Project Euclid: 7 June 2016

zbMATH: 1228.60061
MathSciNet: MR2788892
Digital Object Identifier: 10.1214/ECP.v16-1621

Subjects:
Primary: 60G51
Secondary: 60G57, 60H05

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