American Institute of Mathematical Sciences

A dynamical theory for singular stochastic delay differential equations Ⅱ: nonlinear equations and invariant manifolds

 1 Technische Universität Berlin, Institut für Mathematik, Straße des 17. Juni 136, 10623 Berlin, Germany 2 Sharif University of Technology, Azadi Ave, Tehran, Iran 3 Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Germany

* Corresponding author: Sebastian Riedel

Received  March 2020 Published  October 2020

Building on results obtained in [21], 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 [20].

Citation: Mazyar Ghani Varzaneh, Sebastian Riedel. A dynamical theory for singular stochastic delay differential equations Ⅱ: nonlinear equations and invariant manifolds. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2020304
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