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

   
@article{ECP1621,
	author = {Svend-Erik Graversen and Jan Pedersen},
	title = {Representations of Urbanik's classes and multiparameter Ornstein-Uhlenbeck processes},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {16},
	year = {2011},
	keywords = {Lévy  bases; stochastic integrals;  Urbanik's   classes;  multiparameter Ornstein-Uhlenbeck processes},
	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.},
	pages = {no. 20, 200-212},
	issn = {1083-589X},
	doi = {10.1214/ECP.v16-1621},    
        url = {http://ecp.ejpecp.org/article/view/1621}}