Talk to Stochastic and Non-linear Analysis Seminar

Department of Mathematics

University of Illinois at Urbana-Champaign

  Urbana-Champaign, Illinois,  September  19, 2000; 2:00pm


The talk is titled ``Stochastic Dynamics of Infinite-Dimensional Systems".

Abstract:

We describe an approach to the dynamics of non-linear stochastic differential systems with finite memory using multiplicative cocycles in Hilbert space. We introduce the notion of hyperbolicity for stationary solutions of stochastic systems with memory. We then establish the existence of smooth stable and unstable manifolds in a neighborhood of a hyperbolic stationary solution. The stable and unstable manifolds are stationary and asymptotically invariant under the stochastic semiflow. The proof uses ideas from infinite-dimensional multiplicative ergodic theory and interpolation arguments.

The Lecture:

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    September 13, 2000.