Dynamical properties of Stochastic delay equations

The aim of this talk is investigating the dynamical properties of stochastic delay equation(SDDE) from path-wise point of view ,analyzing the long-time behavior of these equations is quite challenging, since such equations do in general not induce a stochastic flow , However we show (SDDEs) still induce flows on spaces which depend on the current position( spaces of controlled paths) , finally a version of Multiplicative Ergodic Theorem applies and yields the existence of Lyapunov exponents.

Joint work with Dr. Sebastian Riedel