%0 Journal Article
%T Ornstein-Uhlenbeck processes driven by cylindrical L¨¦vy processes
%A Markus Riedle
%J Mathematics
%D 2012
%I arXiv
%X 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.
%U http://arxiv.org/abs/1212.3832v3