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