A dynamical theory for singular stochastic delay differential equations II: Nonlinear equations and invariant manifolds
- Ghani Varzaneh, Mazyar
- Riedel, Sebastian
2010 Mathematics Subject Classification
- 34K19 34K50 37D10 37H15 60H20
- Random dynamical systems, rough paths, stable and unstable manifolds, stochastic delay differential equations
Building 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].
- AIMS Math., 26 (2021), pp. 4587-- 4612, DOI 10.3934/dcdsb.2020304 .