A Dynamical Theory for Singular Stochastic Delay Differential Equations I: Linear Equations and a Multiplicative Ergodic Theorem on Fields of Banach Spaces
DOI10.1137/21M1433435zbMath1490.34103arXiv1903.01172OpenAlexW2970744525WikidataQ113779036 ScholiaQ113779036MaRDI QIDQ5037779
Sebastian Riedel, Mazyar Ghani Varzaneh, Michael K. R. Scheutzow
Publication date: 4 March 2022
Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1903.01172
random dynamical systemsrough pathsmultiplicative ergodic theoremstochastic delay differential equation
Gaussian processes (60G15) Asymptotic theory of functional-differential equations (34K25) Stochastic functional-differential equations (34K50) Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents (37H15) Generation, random and stochastic difference and differential equations (37H10) Stochastic analysis (60H99)
Related Items (5)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A volume-based approach to the multiplicative ergodic theorem on Banach spaces
- Exponential growth rate for a singular linear stochastic delay differential equation
- A Milstein-type scheme without Lévy area terms for SDEs driven by fractional Brownian motion
- A theory of regularity structures
- Pathwise solutions and attractors for retarded SPDEs with time smooth diffusion coefficients
- A concise proof of the multiplicative ergodic theorem on Banach spaces
- A proof of Oseledec's multiplicative ergodic theorem
- Ergodicity of the infinite dimensional fractional Brownian motion
- Differential equations driven by rough paths. Ecole d'Eté de Probabilités de Saint-Flour XXXIV -- 2004. Lectures given at the 34th probability summer school, July 6--24, 2004.
- Delay equations driven by rough paths
- Fibres dynamiques asymptotiquement compacts, exposants de Lyapunov. Entropie. Dimension. (Asymptotically compact dynamical bundles, Lyapunov exponents. Entropy. Dimension)
- Ergodic theory of differentiable dynamical systems
- Characteristic exponents and invariant manifolds in Hilbert space
- Attractors for random dynamical systems
- Random attractors
- Lyapunov exponents of linear stochastic functional differential equations. II: Examples and case studies
- The stable manifold theorem for non-linear stochastic systems with memory. II: The local stable manifold theorem.
- Invariant manifolds for stochastic partial differential equations.
- The stable manifold theorem for stochastic differential equations
- Introduction to the numerical analysis of stochastic delay differential equations
- Controlling rough paths
- Lyapunov exponents of linear stochastic functional differential equations driven by semimartingales. I: The multiplicative ergodic theory
- Rough Burgers-like equations with multiplicative noise
- A dynamical theory for singular stochastic delay differential equations. II: Nonlinear equations and invariant manifolds
- Random dynamical systems, rough paths and rough flows
- El Niño and the delayed action oscillator
- Multidimensional Stochastic Processes as Rough Paths
- Stochastic Differential Delay Equation, Moment Stability, and Application to Hematopoietic Stem Cell Regulation System
- Lyapunov exponents and invariant manifolds for random dynamical systems in a Banach space
- Nonlinear flows of stochastic linear delay equations
- A stochastic delay financial model
- A course on rough paths. With an introduction to regularity structures
This page was built for publication: A Dynamical Theory for Singular Stochastic Delay Differential Equations I: Linear Equations and a Multiplicative Ergodic Theorem on Fields of Banach Spaces