Large Stochastic Resonance and Levy Noise Induced Transitions
The attempt to find a simple qualitative explanation of global glacial cycles led to the ubiquitous random transition paradigm of stochastic resonance. The mathematical frame is given by differential equations with weak periodic signals perturbed by Lévy noise. For white noise, a mathematically rigorous understanding of stochastic resonance uses large deviations for dynamical systems with slow periodic variation.
Analyzing data from the last glacial period reveals an α-stable jump noise component. Since no large deviations theory for dynamical systems perturbed by jump noise is available, the study of transitions requires new methods. Due to the heavy-tail nature of the α-stable component, transition laws differ strongly from the purely white case.
Peter Imkeller, Humboldt University, Berlin, Germany