The stable manifold theorem for non-linear stochastic systems with memory. II: The local stable manifold theorem.

DOI10.1016/j.jfa.2003.06.002zbMath1053.60061OpenAlexW1594115232MaRDI QIDQ1423432

Salah-Eldin A. Mohammed, Michael K. R. Scheutzow

Publication date: 14 February 2004

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2003.06.002

zbMATH Keywords

stochastic functional differential equationlocal stable manifoldsstochastic semiflowstationary hyperbolic trajectory

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Random operators and equations (aspects of stochastic analysis) (60H25) Stochastic integral equations (60H20)

Related Items (13)

A Dynamical Theory for Singular Stochastic Delay Differential Equations I: Linear Equations and a Multiplicative Ergodic Theorem on Fields of Banach Spaces ⋮ Global stability of stationary solutions for a class of semilinear stochastic functional differential equations with additive white noise ⋮ Moment boundedness of linear stochastic delay differential equations with distributed delay ⋮ DECAY AND GROWTH RATES OF SOLUTIONS OF SCALAR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY AND STATE DEPENDENT NOISE ⋮ EXPONENTIAL GROWTH RATES FOR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS ⋮ Second moment boundedness of linear stochastic delay differential equations ⋮ The substitution theorem for semilinear stochastic partial differential equations ⋮ Growth and fluctuation in perturbed nonlinear Volterra equations ⋮ Dynamics of stochastic 2D Navier-Stokes equations ⋮ Stochastic Volterra equations in weighted spaces ⋮ A dynamical theory for singular stochastic delay differential equations. II: Nonlinear equations and invariant manifolds ⋮ Persistence of Homoclinic Orbits under White Noise Perturbation ⋮ Sobolev differentiable stochastic flows for SDEs with singular coefficients: applications to the transport equation

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