Abstract by Junyilang Zhao
Invariant Manifolds and Foliations for a Random Differential Equation
We consider the random differential equation, du/dt=Au+f(u)+g(u) (W(t+delta)-W(t))/delta, which is an approximation for a stochastic differential equation with the same structure. Here W is a Hilbert space valued Wiener process. We show that under certain hypotheses on A, f, and g, there exist local invariant manifolds and foliations for this system, which are indeed given by smooth local graphs. Further applications are to be suggested as well.