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The Center for Control, Dynamical Systems, and Computation University of California at Santa Barbara
 

Summary: The Center for Control, Dynamical Systems, and Computation
University of California at Santa Barbara
Winter 2010 Seminar Series
Presents
Spectral Theory and Model Reduction for Markov Models
Sean Meyn
Department of Electrical and Computer Engineering
University of Illinois
Friday, January 8, 2009, 3:00 4:00pm CHEM 1171
Abstract: We survey recent approaches to model reduction for Markov models based on spectral
theory. The approximating process is described as a hidden Markov model (HMM) with finite state
space. These approximations are possible under a Lyapunov drift condition introduced by Donsker-
Varadahn in their treatment of large deviations for diffusions. In the special case of diffusions, we find
that eigen functions provide a decomposition of the state space into "almost invariant" sets. The diffu-
sion mixes rapidly in each of these subsets prior to exiting, and the exit time from one of these sets is
approximately exponential.
About the Speaker: Sean Meyn received the B.A. degree in Mathematics Summa Cum Laude
from UCLA in 1982 and the PhD degree in Electrical Engineering from McGill University in 1987 (with
Prof. P. Caines, McGill University). After a two year postdoctoral fellowship at the Australian National
University in Canberra, Dr. Meyn and his family moved to the Midwest. He is now a Professor in the

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics