Talk to Ellis B. Stouffer Colloquium

Department of Mathematics

 University of Kansas

Lawrence, Kansas, October 1, 1998; 4:00pm

This talk is titled On the Dynamics of Stochastic Differential Equations . Here is an abstract:

We formulate and outline a proof of the Local Stable Manifold Theorem for stochastic differential equations (SDE's) in Euclidean space (joint work with M. Scheutzow). This is a central result in dynamical systems with noise. Starting with the existence of a stochastic flow for an SDE, we introduce the notion of a hyperbolic stationary trajectory. We prove the existence of invariant random stable and unstable manifolds in the neighborhood of a hyperbolic stationary solution. For Stratonovich noise, the stable and unstable manifolds are dynamically characterized using forward and backward solutions of the anticipating SDE.

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    Department of Mathematics, University of Kansas

    Salah's Home Page

    September 30, 1998.