Ornstein-Uhlenbeck processes driven by cylindrical Levy processes

Anita Behme, TUD, Institute of Stochastics; Markus Riedle, King’s, Department of Mathematics

Research area: Mathematics

The transCampus Professors Anita Behme (TU Dresden) and Markus Riedle (King’s College London) have received a DFG grant for their project “Ornstein-Uhlenbeck processes driven by cylindrical Levy processes” which includes a 3-year PhD studentship. The PhD student will be provided with tandem supervision from both locations, with the experience of internationally competitive research and with the opportunity to develop an international network. To further support the project, the transCampus initiative provides additional funding for the studies carried out at King’s.

The research areas of both supervisors confluence in the project. During the time in Dresden the PhD student will concentrate on modelling aspects of the project which represents Anita Behme’s field of expertise, whereas the focus will be on the analytical part during the stay in London supervised by Markus Riedle. The corporate project of both transCampus professors studies a complex dynamical system evolving in time and space that is subject to a random perturbation. Such models arise naturally in various field such as engineering, economics and physics among many others. External or internal fluctuations, not allowing a deterministic description, in random events in the future, or in uncertainty of the model. Up to now, modelling the random perturbations has been restricted to rather regular processes although statistical evidence, experimental observations or realistic constraints require the perturbation by a highly irregular process such as a cylindrical Levy process. One might just think of the sudden slip on a fault which causes an earthquake.