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2015 Infinite dimensional Ornstein-Uhlenbeck processes driven by Lévy processes
David Applebaum
Probab. Surveys 12: 33-54 (2015). DOI: 10.1214/14-PS249


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.


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David Applebaum. "Infinite dimensional Ornstein-Uhlenbeck processes driven by Lévy processes." Probab. Surveys 12 33 - 54, 2015.


Received: 1 November 2014; Published: 2015
First available in Project Euclid: 20 August 2015

zbMATH: 1323.60104
MathSciNet: MR3385977
Digital Object Identifier: 10.1214/14-PS249

Primary: 60G51
Secondary: 60E07 , 60H10 , 60H15 , 60J80

Keywords: branching property , cylindrical process , invariant measure , Lévy process , Mehler semigroup , operator self–decomposability , Ornstein-Uhlenbeck process , skew–convolution semigroup , Urbanik semigroup

Rights: Copyright © 2015 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.12 • 2015
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