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- ItemA dynamical theory for singular stochastic delay differential equations II: Nonlinear equations and invariant manifolds(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Ghani Varzaneh, Mazyar; Riedel, SebastianBuilding on results obtained in [GVRS], we prove Local Stable and Unstable Manifold Theorems for nonlinear, singular stochastic delay differential equations. The main tools are rough paths theory and a semi-invertible Multiplicative Ergodic Theorem for cocycles acting on measurable fields of Banach spaces obtained in [GVR].
- ItemInvariant manifolds for random dynamical systems with slow and fast variables(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Schmalfuss, Björn; Schneider, Klaus R.We consider random dynamical systems with slow and fast variables driven by two independent metric dynamical systems modelling stochastic noise. We establish the existence of a random inertial manifold eliminating the fast variables. If the scaling parameter tends to zero, the inertial manifold tends to another manifold which is called the slow manifold. We achieve our results by means of a fixed point technique based on a random graph transform. To apply this technique we need an asymptotic gap condition.