Infinite Dimensional Ornstein-Uhlenbeck Processes Driven by Levy Processes

David Applebaum

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arXiv · 1411.2752

Infinite Dimensional Ornstein-Uhlenbeck Processes Driven by Levy Processes

David Applebaum

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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.

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David Applebaum. 2014-11-11. Infinite Dimensional Ornstein-Uhlenbeck Processes Driven by Levy Processes. https://arxiv.org/abs/1411.2752

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