Ornstein-Uhlenbeck processes driven by cylindrical Lévy processes

• Applicants: Professorin Dr. Anita Behme; Professor Dr. Markus Riedle
• Subject Area: Mathematics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 504592679

Cylindrical Brownian motion, or equivalently space-time white noise, is a standard model for Gaussian and continuous random perturbations of dynamical systems in infinite dimensional spaces, such as partial differential equations. They are naturally extended to cylindrical Lévy processes allowing to model discontinuous, non-Gaussian and highly irregular random perturbations. This project considers Ornstein-Uhlenbeck processes driven by cylindrical Lévy processes, i.e. solutions of stochastic linear partial differential equations with additive noise modelled by a cylindrical Lévy process. It has been observed that these processes may exhibit properties which were not observed in the finite-dimensional space or in case of more regular perturbations, e.g highly irregular paths. In this project, fundamental properties of Ornstein-Uhlenbeck processes driven by cylindrical Lévy processes will be studied, such as e.g. path properties and the strong or asymptotically strong Feller property. Moreover, these results will be used to define and study a generalisation of the Lévy-driven Ornstein-Uhlenbeck process in the infinite dimensional space.

• DFG Programme: Research Grants