Rate of convergence to equilibrium of fractional driven stochastic differential equations with rough multiplicative noise

DOI10.1214/18-AOP1265zbMath1440.60028arXiv1605.00880OpenAlexW2904923868WikidataQ128747126 ScholiaQ128747126MaRDI QIDQ1731893

Aurélien Deya, Samy Tindel, Fabien Panloup

Publication date: 14 March 2019

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.00880

zbMATH Keywords

Lyapunov functionfractional Brownian motionstochastic differential equationsergodicitymultiplicative noisetotal variation distancerate of convergence to equilibrium

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Ergodicity, mixing, rates of mixing (37A25)

Related Items (8)

Random dynamical systems, rough paths and rough flows ⋮ On the (non)stationary density of fractional-driven stochastic differential equations ⋮ Rate of convergence to equilibrium of fractional driven stochastic differential equations with rough multiplicative noise ⋮ First-order Euler scheme for SDEs driven by fractional Brownian motions: the rough case ⋮ Asymptotical stability of differential equations driven by Hölder continuous paths ⋮ Rate of convergence to equilibrium for discrete-time stochastic dynamics with memory ⋮ Sub-exponential convergence to equilibrium for Gaussian driven stochastic differential equations with semi-contractive drift ⋮ Slow-fast systems with fractional environment and dynamics

Cites Work

• Unnamed Item
• Unnamed Item
• The Jain-Monrad criterion for rough paths and applications to random Fourier series and non-Markovian Hörmander theory
• Regularity of laws and ergodicity of hypoelliptic SDEs driven by rough paths
• Approximation of stationary solutions of Gaussian driven stochastic differential equations
• Asymptotic coupling and a general form of Harris' theorem with applications to stochastic delay equations
• Discretization of stationary solutions of stochastic systems driven by fractional Brownian motion
• Almost sure exponential behavior of a directed polymer in a fractional Brownian environment
• Non-Markovian invariant measures are hyperbolic
• Exponential convergence for the stochastically forced Navier-Stokes equations and other partially dissipative dynamics
• Stochastic calculus with respect to fractional Brownian motion with Hurst parameter lesser than 1/2
• Rate of convergence to equilibrium of fractional driven stochastic differential equations with rough multiplicative noise
• A priori estimates for rough PDEs with application to rough conservation laws
• Ergodicity of stochastic differential equations driven by fractional Brownian motion
• Controlling rough paths
• Exponential and uniform ergodicity of Markov processes
• Stochastic modeling in nanoscale biophysics: subdiffusion within proteins
• Rate of convergence to equilibrium of fractional driven stochastic differential equations with some multiplicative noise
• Ergodic theory for SDEs with extrinsic memory
• Spectral gaps in Wasserstein distances and the 2D stochastic Navier-Stokes equations
• Approximation of stationary solutions to SDEs driven by multiplicative fractional noise
• Multidimensional Stochastic Processes as Rough Paths
• Differential Equations Driven by Rough Paths: An Approach via Discrete Approximation
• Analysis and Geometry of Markov Diffusion Operators
• NO ARBITRAGE UNDER TRANSACTION COSTS, WITH FRACTIONAL BROWNIAN MOTION AND BEYOND
• A course on rough paths. With an introduction to regularity structures
• Weak Poincaré inequalities and \(L^2\)-convergence rates of Markov semigroups

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