The stable manifold theorem for non-linear stochastic systems with memory. I: Existence of the semiflow.

DOI10.1016/j.jfa.2002.04.001zbMath1039.60060OpenAlexW2068495549MaRDI QIDQ1421847

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

Publication date: 3 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.2002.04.001

zbMATH Keywords

stochastic functional differential equationstochastic semiflow

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stochastic integral equations (60H20)

Related Items (25)

Anticipating stochastic differential systems with memory ⋮ An elementary humanomics approach to boundedly rational quadratic models ⋮ Fractional dynamical system and its linearization theorem ⋮ Global stability of stationary solutions for a class of semilinear stochastic functional differential equations with additive white noise ⋮ Quasimonotone random and stochastic functional differential equations with applications ⋮ The Burgers equation with affine linear noise: dynamics and stability ⋮ Moment boundedness of linear stochastic delay differential equations with distributed delay ⋮ Speculative and hedging interaction model in oil and U.S. dollar markets -- phase transition ⋮ Retarded evolution systems driven by fractional Brownian motion with Hurst parameter \(H>1/2\) ⋮ The stable manifold theorem for non-linear stochastic systems with memory. II: The local stable manifold theorem. ⋮ EXPONENTIAL GROWTH RATES FOR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS ⋮ Pathwise solutions and attractors for retarded SPDEs with time smooth diffusion coefficients ⋮ Second moment boundedness of linear stochastic delay differential equations ⋮ Growth and fluctuation in perturbed nonlinear Volterra equations ⋮ Flow of diffeomorphisms for SDEs with unbounded Hölder continuous drift ⋮ Lack of strong completeness for stochastic flows ⋮ A dynamical theory for singular stochastic delay differential equations. II: Nonlinear equations and invariant manifolds ⋮ Persistence of Homoclinic Orbits under White Noise Perturbation ⋮ A Stochastic Gronwall Lemma and Well-Posedness of Path-Dependent SDEs Driven by Martingale Noise ⋮ Speculative and hedging interaction model in oil and U.S. dollar markets -- long-term investor dynamics and phases ⋮ A note on the generation of random dynamical systems from fractional stochastic delay differential equations ⋮ Heavy-tailed distributions of volume and price-change resulting from strategy coordination and decision noise ⋮ Global well-posedness of stochastic nematic liquid crystals with random initial and boundary conditions driven by multiplicative noise ⋮ Sobolev differentiable stochastic flows for SDEs with singular coefficients: applications to the transport equation ⋮ Global well-posedness of stochastic 2D primitive equations with random initial conditions

Cites Work

• Semimartingales and measure preserving flows
• Large deviations and stochastic flows of diffeomorphisms
• Characteristic exponents and invariant manifolds in Hilbert space
• Spatial estimates for stochastic flows in Euclidean space
• Perfect cocycles through stochastic differential equations
• Lyapunov exponents of linear stochastic functional differential equations. II: Examples and case studies
• On the spatial asymptotic behavior of stochastic flows in Euclidean space
• The stable manifold theorem for stochastic differential equations
• Lyapunov exponents of linear stochastic functional differential equations driven by semimartingales. I: The multiplicative ergodic theory
• Stochastic flows for nonlinear second-order parabolic SPDE
• Stochastic parabolic equations in bounded domains: random evolution operator and lyapunov exponents
• A generalized formula of Ito and some other properties of stochastic flows
• The lyapunov spectrum and stable manifolds for stochastic linear delay equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The stable manifold theorem for non-linear stochastic systems with memory. I: Existence of the semiflow.