Introduction to Cylindrical Lévy processes: Part II (Markus Riedle)
The webinars will take place on Zoom and a link to the virtual room will be sent out to all those who registered at the registration page.
Speaker: Markus Riedle (Kings College London)
Title: Introduction to Cylindrical Lévy processes
Abstract: Cylindrical Lévy processes are a natural extension of cylindrical Brownian motion which has been the standard model of random perturbations of partial differential equations and other models in infinite dimensions for the last 50 years. Here, the attribute cylindrical refers to the fact that cylindrical Brownian motions are not classical stochastic processes attaining values in the underlying space but are generalised objects. The reasons for the choice of cylindrical but not classical Brownian motion can be found in the facts that there does not exist a classical Brownian motion with independent components in an infinite dimensional Hilbert space, and that cylindrical processes enable a very flexible modelling of random noise in time and space.
In this lecture series, we briefly present some aspects of the theory of cylindrical measures and cylindrical random variables. We introduce cylindrical Lévy processes and present some specific examples in detail and discuss their relations to other models of random perturbations in the literature. We present a theory of stochastic integration with respect to cylindrical random variables, which cannot rely on the classical approach, as cylindrical Lévy processes do not enjoy a semi-martingale decomposition. We finish this lecture series by investigating some specific models driven by cylindrical Lévy processes, such as Ornstein-Uhlenbeck processes.
This series of webinars addresses all interested people in probability, stochastic analysis, control, risk evaluation, statistics, with a view towards applications, in particular to renewable energy markets and production. This series brings together the major research themes of the projects STORM, SCROLLER, and SPATUS.