WIAS Preprint No. 2701, (2020)

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


Authors

  • Ghani Varzaneh, Mazyar
  • Riedel, Sebastian

2010 Mathematics Subject Classification

  • 34K19 34K50 37D10 37H15 60H20

Keywords

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

DOI

10.20347/WIAS.PREPRINT.2701

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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