Im Rahmen des BGTS Kolloquiums trägt Peter Imkeller von der HU Berlin vor.
Titel: Paleoclimatic time series: dynamics and statistics
Abstract: Simple models of the earth’s energy balance are instrumental for interpreting some qualitative aspects of the dynamics of paleo-climatic data. In the 1980s this led to the investigation of periodically forced dynamical systems of the reaction-diffusion type with small Gaussian noise, and a rough explanation of glacial cycles by Gaussian meta-stability.
A spectral analysis of Greenland ice time series performed at the end of the 1990s representing average temperatures during the last ice age suggest an α-stable noise component with an α ~ 1.75. Based on this observation, papers in the physics literature attempted an interpretation featuring dynamical systems perturbed by small Lévy noise.
In terms of statistics of stochastic processes, this leads to a model selection problem. As an example of a possible low dimensional model class we describe the time series as a simple dynamical system perturbed by α-stable noise. One needs an efficient test for the best fitting α. We discuss a statistical testing method based on the p-variation of the solution trajectories of SDE with Lévy noise.
(joint work with J. Gairing, C. Hein, M. Högele, I. Pavlyukevich)
