Peter Imkeller| Department of Mathematics, Humboldt-Universität zu Berlin
Model selection for paleo-climatic time series: stable and fractional noise
Dynamical systems of the reaction-diﬀusion type with small noise have been instrumental to explain basic features of the dynamics of paleo-climate data. For instance, 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 com-ponent with an α ∼ 1.75. On the other hand, strong memory eﬀects in the dynamics of global average temperatures are attributed to the global cryosphere. We model the time series as a dynamical system perturbed by α-stable and fractional Gaussian noise, and develop an eﬃcient testing method for the best ﬁtting α resp. Hurst coeﬃcient. The method is based on the observed power variations of the residuals of the time series. Their asymptotic behavior in case of α-stable noise is described by a/p-stable processes, while in the fractional Gaussian case normal asymptotic behavior is observed for suitably renormalized approximations of the quadratic variation. This talk is based on joint work with J. Gairing, C. Hein, C. Tudor.
Professor Peter Imkeller received his Ph.D. in 1982 and his award-winning Habilitation in 1987, both from the Ludwig-Maximilians-Universität at Munich. He was a Heisenberg Scholar during 1988. He became Professor of Mathematics in 1993 and moved to Humboldt-Universität zu Berlin as the Professor for Stochastic Analysis in 1996. His list of publications contains several books and more than 140 papers. His main fields of research are stochastic analysis, random dynamical systems, stochastic stability and bifurcation, stochastic climate models and stochastic finance.