### Talk at Probability and Mathematical Physics Seminar

#### University of California at Irvine

The talk described recent joint work with Michael Scheutzow.
For a preprint, please see Recent Articles and
Preprints Online.
To download a .dvi file of the lecture, click on the following:

The Lecture

*THE STABLE MANIFOLD THEOREM FOR SDE'S: Abstract *

*Tuesday, March 3, 1998, 2:00-3:00 pm, Room PSI 314. *

In this talk, we formulate a local stable manifold theorem for stochastic
differential equations in Euclidean space, driven by multi-dimensional
Brownian motion. We introduce the concept of hyperbolicity for stationary
trajectories of a SDE. This is done using the Oseledec muliplicative ergodic
theorem on the linearized SDE along the stationary solution. Using methods
of (non-linear ergodic theory), we construct a stationary family of stable
and unstable manifolds in a stationary neighborhood around the hyperbolic
stationary trajectory of the non-linear SDE. The stable/unstable manifolds
are dynamically characterized using anticipative stochastic calculus.

*
Salah's Home Page *

*March 5, 1998.*