Cylindrical Levy processes
Speaker:Dr. Markus Riedle
Reader in Probability, Statistics and Financial Mathematics
King's College London, UK
Date & Time:25 Mar 2015 (Wednesday) 10:00 - 11:00
Venue:E11-1040
Organized by:Department of Mathematics

Abstract

The objective of this talk is the introduction of cylindrical Levy processes and their stochastic integrals in Hilbert spaces.

The degree of freedom of models in infinite dimensions is often reacted by the request that each mode along a dimension is independently perturbed by the noise. In the Gaussian setting, this leads to the cylindrical Wiener process including from a model point of view the very important possibility to model a Gaussian noise in both time and space in a great edibility (space-time white noise). Up to very recently, there has been no analogue for Levy processes.

Based on the classical theory of cylindrical processes and cylindrical measures we introduce cylindrical Levy processes as a natural generalisation of cylindrical Wiener processes. We illustrate our abstract approach by several specific examples of cylindrical Levy processes. We continue to characterise the distribution of cylindrical Levy processes by a cylindrical version of the Levy-Khintchine formula. The last part of the talk is devoted to explain the difficulty to introduce a stochastic integral with respect to cylindrical Levy processes, and how we could solve this problem.

(parts of this talk are based on joint work with D. Applebaum or A. Jakubowski)

Biography

Prof. Markus Riedle received his Ph.D. from Humboldt University Berlin in 2003 where he continued to hold a postdoctoral position. In the academic year 2006-07 he substituted a professor position in applied mathematics at the University of Mannheim, before he was appointed as a lecturer at the University of Manchester in 2007. He joined King's College London as a Reader in 2011.