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 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.