Long-time behaviour of stochastic delay equations

Monday 27th February 2012 – 14:15 to 15:15

Speaker: Michael Scheutzow (TU Berlin)

First we provide a survey on the long-time behaviour of stochastic delay equations with bounded memory, addressing existence and uniqueness of invariant measures, Lyapunov spectra, and exponential growth rates.

Then, we study the very simple one-dimensional equation $dX(t)=X(t-1)dW(t)$ in more detail and establish the existence of a deterministic exponential growth rate of a suitable norm of the solution via a Furstenberg-Hasminskii-type formula.

Parts of the talk are based on joint work with Martin Hairer and Jonathan Mattingly.

Part of the Stochastic Analysis Seminar Series