Stochastic Lattice Dynamical Systems with Fractional Noise

DOI10.1137/16M1085504zbMath1368.60065arXiv1609.02543MaRDI QIDQ5737795

Xiaoying Han, María J. Garrido-Atienza, Hakima Bessaih, Björn Schmalfuss

Publication date: 30 May 2017

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.02543

zbMATH Keywords

exponential stabilitypathwise solutionsstochastic lattice equationsHilbert-valued fractional Brownian motion

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Infinite-dimensional random dynamical systems; stochastic equations (37L55)

Related Items (23)

Optimization and Convergence of Numerical Attractors for Discrete-Time Quasi-Linear Lattice System ⋮ Nontrivial Equilibrium Solutions and General Stability for Stochastic Evolution Equations with Pantograph Delay and Tempered Fractional Noise ⋮ Synchronization of stochastic lattice equations and upper semicontinuity of attractors ⋮ The local exponential stability of evolution equation driven by Hölder-continuous paths ⋮ Exponential stability of stochastic evolution equations driven by small fractional Brownian motion with Hurst parameter in \((1/2,1)\) ⋮ Synchronization of stochastic lattice equations ⋮ Ergodicity and approximations of invariant measures for stochastic lattice systems with Markovian switching ⋮ Convergence rate of synchronization of coupled stochastic lattice systems with additive fractional noise ⋮ New results for stochastic fractional pseudo-parabolic equations with delays driven by fractional Brownian motion ⋮ Enlarged Numerical Attractors for Lattice Systems with Porous Media Degeneracies ⋮ Existence of smooth stable manifolds for a class of parabolic SPDEs with fractional noise ⋮ Unnamed Item ⋮ Analysis of a stochastic SIR model with fractional Brownian motion ⋮ Asymptotic autonomous attractors for a stochastic lattice model with random viscosity ⋮ Uniform attractors for a class of stochastic evolution equations with multiplicative fractional noise ⋮ Regularity and backward compactness of attractors for non-autonomous lattice systems with random coefficients ⋮ Local Stability of Differential Equations Driven by Hölder-Continuous Paths with Hölder Index in (1/3,1/2) ⋮ Pathwise solution to rough stochastic lattice dynamical system driven by fractional noise ⋮ Limiting behavior of invariant measures of highly nonlinear stochastic retarded lattice systems ⋮ Wong–Zakai approximations and random attractors of non-autonomous stochastic discrete complex Ginzburg–Landau equations ⋮ Periodic solutions in distribution of stochastic lattice differential equations ⋮ Attractors for multi-valued lattice dynamical systems with nonlinear diffusion terms ⋮ Limit measures of stochastic Schrödinger lattice systems

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