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SUMMARY:Paleo-climatic time series: statistics and dynamics - Imkeller\, P
  (Humboldt-Universitt zu Berlin)
DTSTART:20131029T101000Z
DTEND:20131029T104500Z
UID:TALK48546@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Co-authors: Arnaud Debussche (ENS Cachan)\, Jan Gairing (HU Be
 rlin)\, Claudia Hein (HU Berlin)\, Michael Hgele (U Potsdam)\, Ilya Pavlyu
 kevich (U Jena) \n\nDynamical systems of the reaction-diffusion type with 
 small noise have been instrumental to explain basic features of the dynami
 cs of paleo-climate data. For instance\, a spectral analysis of Greenland 
 ice time series performed at the end of the 1990s representing average tem
 peratures during the last ice age suggest an $lpha-$stable noise componen
 t with an $lpha im 1.75.$ We model the time series as a dynamical system 
 perturbed by $lpha$-stable noise\, and develop an efficient testing metho
 d for the best fitting $lpha$. The method is based on the observed $p$-va
 riation of the residuals of the time series\, and their asymptotic $rac{
 lpha}{p}$-stability established in local limit theorems.par mallskip\n\nGe
 neralizing the solution of this model selection problem\, we are led to a 
 class of reaction-diffusion equations with additive $lpha$-stable L'evy n
 oise\, a stochastic perturbation of the Chafee-Infante equation. We study 
 exit and transition between meta-stable states of their solutions. Due to 
 the heavy-tail nature of an $lpha$-stable noise component\, the results d
 iffer strongly from the well known case of purely Gaussian perturbations.\
 n
LOCATION:Seminar Room 1\, Newton Institute
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