Seminar series
Date
Mon, 27 Feb 2012
Time
14:15 -
15:15
Location
Oxford-Man Institute
Speaker
Michael Scheutzow
Organisation
TU Berlin
Abstract: 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.