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

Discrete and Continuous Dynamical Systems-series B（2017）

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摘要

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 ].

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关键词

Random dynamical systems, rough paths, stable and unstable manifolds, stochastic delay differential equations

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