Infinite Dimensional Ornstein-Uhlenbeck Processes Driven by Levy Processes
Probability
2014-11-12 v1
Abstract
We review the probabilistic properties of Ornstein-Uhlenbeck processes in Hilbert spaces driven by L\'{e}vy 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.
Cite
@article{arxiv.1411.2752,
title = {Infinite Dimensional Ornstein-Uhlenbeck Processes Driven by Levy Processes},
author = {David Applebaum},
journal= {arXiv preprint arXiv:1411.2752},
year = {2014}
}