###
Talk to Probability Seminar

###
Institut Elie Cartan

###
Universite' Henri Poincare' Nancy 1

####
Nancy, France, June 17, 1999; 10:30am

The talk is titled ``The Stable Manifold Theorem for Stochastic Systems
with Memory".
####
Abstract:

We state and prove a *Local Stable Manifold Theorem *for nonlinear
stochastic differential systems with finite memory (viz. stochastic functional
differential equations (sfde's)). We introduce the notion of hyperbolicity
for stationary solutions of sfde's. 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
infinite-dimensional multiplicative ergodic theory techniques and interpolation
arguments.
####
The Lecture:

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

compressed postscript file
(259K)
postscript file (uncompressed)
(1051K)
compressed dvi file (200K)
dvi file (uncompressed) (305K)

*Institut de Mathématiques
Élie Cartan, Universite' Henri Poincare' Nancy 1, Nancy, France*

*
Salah's Home Page*

*October 11, 1999.*