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

Mazyar Ghani Varzaneh; Sebastian Riedel

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arXiv · 2003.03202

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

Mazyar Ghani Varzaneh·Sebastian Riedel

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Abstract

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].

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Mazyar Ghani Varzaneh, Sebastian Riedel. 2020-03-05. A dynamical theory for singular stochastic delay differential equations II: Nonlinear equations and invariant manifolds. https://arxiv.org/abs/2003.03202

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