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


 
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1. Title Title of document Representations of Urbanik's classes and multiparameter Ornstein-Uhlenbeck processes
 
2. Creator Author's name, affiliation, country Svend-Erik Graversen; Aarhus University
 
2. Creator Author's name, affiliation, country Jan Pedersen; Aarhus University
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Lévy bases; stochastic integrals; Urbanik's classes; multiparameter Ornstein-Uhlenbeck processes
 
3. Subject Subject classification 60G51; 60G57; 60H05
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2011-04-18
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1621
 
10. Identifier Digital Object Identifier 10.1214/ECP.v16-1621
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 16
 
12. Language English=en
 
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