Humboldt-Universität zu Berlin - Mathematisch-Naturwissen­schaft­liche Fakultät - International Research Training Group 1740

Video Conference

Dr. Michael Högele (Universität Potsdam, Project 18)

Title: The first exit problem for Gaussian and non-Gaussian Lévy diffusions motivated by paleoclimate data

The first exit problem (FEP) for (Gaussian and non-Gaussian) Lévy diffusions from a vicinity of a stable state at small noise intensity provides important conceptual insight in paleoclimatic climate fluctuations. A prominent example are &alpha-stable diffusions which arise in the statistical analysis of time series of the last glacial period, both in the physical and in the mathematical literature.
After a climatological motivation, we will explain the notion and basic features of (Gaussian and non-Gaussian) Lévy processes and diffusions and adress the corresponding FEP. In the Gaussian case the first exit problem is well-known for a long time and we will review it briefly. The case of finite-dimensional systems with additive and multiplicative non-Gaussian Lévy noise was studied in the last years by Imkeller, Pavlyukevich and collaborators and by Debussche, Högele and Imkeller for non-linear reaction diffusion equations, such as the Chafee-Infante equation.
In this talk we will present a general result about the asymptotic first exit time problem of regularly varying Lévy diffusions to leave the vicinity of a global attractor and compare it to the Gaussian case. This is joint work with I. Pavlyukevich, FSU Jena.