Random attractors for dissipative systems with rough noises

DOI10.3934/dcds.2021176zbMath1496.37051OpenAlexW3112605337MaRDI QIDQ2078359

Luu Hoang Duc

Publication date: 28 February 2022

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2021176

zbMATH Keywords

stochastic differential equationsrandom dynamical systemsstochastic stabilityrandom attractorsrough path theorystochastic perturbationrough integrals

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stopping times; optimal stopping problems; gambling theory (60G40) Generation, random and stochastic difference and differential equations (37H10) Stability theory for random and stochastic dynamical systems (37H30)

Related Items

Numerical Attractors for Rough Differential Equations ⋮ Random attractors for rough stochastic partial differential equations ⋮ Wong-Zakai type approximations of rough random dynamical systems by smooth noise

Cites Work

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• Local pathwise solutions to stochastic evolution equations driven by fractional Brownian motions with Hurst parameters \(H\in (1/3,1/2\)]
• Rough differential equations with unbounded drift term
• Regularity of laws and ergodicity of hypoelliptic SDEs driven by rough paths
• Integrability and tail estimates for Gaussian rough differential equations
• Selected aspects of fractional Brownian motion.
• Nonautonomous and random attractors
• Ergodicity of hypoelliptic SDEs driven by fractional Brownian motion
• Stochastic stability of differential equations. With contributions by G. N. Milstein and M. B. Nevelson
• 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.
• An extension of the concept of gradient semigroups which is stable under perturbation
• Upper semicontinuity of the attractor for a singularly perturbed hyperbolic equation
• On the gap between deterministic and stochastic ordinary differential equations
• Differential equations driven by rough signals
• Attractors for random dynamical systems
• Nonautonomous Young differential equations revisited
• Exponential stability of stochastic evolution equations driven by small fractional Brownian motion with Hurst parameter in \((1/2,1)\)
• Ergodicity of stochastic differential equations driven by fractional Brownian motion
• Controlling rough paths
• Local mild solutions for rough stochastic partial differential equations
• Random dynamical systems, rough paths and rough flows
• Ergodic theory for SDEs with extrinsic memory
• Existence and upper semicontinuity of attractors for stochastic equations with deterministic non-autonomous terms
• RANDOM ATTRACTORS FOR STOCHASTIC EQUATIONS DRIVEN BY A FRACTIONAL BROWNIAN MOTION
• Multidimensional Stochastic Processes as Rough Paths
• Rough path analysis via fractional calculus
• Upper semicontinuity of attractors for small random perturbations of dynamical systems
• Asymptotic Stability for Stochastic Dissipative Systems with a Hölder Noise
• Fractional Brownian Motions, Fractional Noises and Applications
• A course on rough paths. With an introduction to regularity structures
• The conjugacy of stochastic and random differential equations and the existence of global attractors