Abstract #300414

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JSM 2002 Abstract #300414
Activity Number: 26
Type: Invited
Date/Time: Sunday, August 11, 2002 : 4:00 PM to 5:50 PM
Sponsor: IMS
Abstract - #300414
Title: Theory & Application of Geometric Ergodicity since the Big Red Book
Author(s): Sean Meyn*+
Affiliation(s): University of Illinois
Address: 1308 W. Main Street, Urbana, Illinois, 61801, USA
Keywords: Spectral Theory ; Markov chains ; Large deviations theory
Abstract:

Much of the author's research collaboration with Richard Tweedie concerned characterizations of geometric ergodicity for Markov chains and ergodic theorems for this very general class of processes.

This talk will review the function-analytic setting developed in (A) for analysing geometrically ergodic Markov chains, and survey recent findings. Topics to be discussed include: 1.) spectral theory and the V-uniform ergodic theorem; 2.) the multiplicative Poisson equation; 3.) multiplicative ergodic theory; 4.) products of random matrices; and 5.) exact large deviations.

(A) S.P. Meyn and R.L. Tweedie. Markov Chains and Stochastic Stability, Springer-Verlag, London, 1993.

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