Infinite dimensional Ornstein-Uhlenbeck processes driven by Lévy processes
Applebaum, D.
(2015)
Infinite dimensional Ornstein-Uhlenbeck processes driven by Lévy processes.
Probability Surveys, 12 (2015).
33 - 54.
ISSN 1549-5787
Abstract
We review the probabilistic properties of Ornstein-Uhlenbeck processes in Hilbert spaces driven by Lévy processes. The emphasis is on the different contexts in which these processes arise, such as stochastic partial differential equations, continuous-state branching processes, generalised Mehler semigroups and operator self-decomposable distributions. We also examine generalisations to the case where the driving noise is cylindrical.
Metadata
Item Type:
Article
Authors/Creators:
Applebaum, D.
Copyright, Publisher and Additional Information:
This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (http://creativecommons.org/licenses/by/2.5/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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