Ornstein-Uhlenbeck processes driven by cylindrical L\'evy processes
Abstract
In this article we introduce a theory of integration for deterministic, operator-valued integrands with respect to cylindrical L\'evy processes in separable Banach spaces. Here, a cylindrical L\'evy process is understood in the classical framework of cylindrical random variables and cylindrical measures, and thus, it can be considered as a natural generalisation of cylindrical Wiener processes or white noises. Depending on the underlying Banach space, we provide necessary and/or sufficient conditions for a function to be integrable. In the last part, the developed theory is applied to define Ornstein-Uhlenbeck processes driven by cylindrical L\'evy processes and several examples are considered.
Keywords
Cite
@article{arxiv.1212.3832,
title = {Ornstein-Uhlenbeck processes driven by cylindrical L\'evy processes},
author = {Markus Riedle},
journal= {arXiv preprint arXiv:1212.3832},
year = {2014}
}
Comments
This version is significantly revised and corrected