### 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.

To download the lecture, please click on one of the following:

dvi file (411K)
postscript file (uncompressed, 1174K)
compressed postscript file (295K )

*
Department of Mathematics, University of Kansas *

*
Salah's Home Page *

*September 30, 1998.*