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

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.

Citation

Download Citation

David Applebaum. "Infinite dimensional Ornstein-Uhlenbeck processes driven by Lévy processes." Probab. Surveys 12 33 - 54, 2015. https://doi.org/10.1214/14-PS249

Information

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

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

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

JOURNAL ARTICLE
22 PAGES


SHARE
Vol.12 • 2015
Back to Top