This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Ghani Varzaneh, MazyarRiedel, Sebastian2022-06-302022-06-302020https://oa.tib.eu/renate/handle/123456789/9351https://doi.org/10.34657/8389Building 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].eng510Random dynamical systemsrough pathsstable and unstable manifoldsstochastic delay differential equationsReport23 S.