13 citations · 24 across the 11 of their papers we have counts for
16 papers
Rough Path Theory to approximate Random Dynamical Systems
Hongjun Gao, María J. Garrido-Atienza, Anhui Gu +2
We consider the rough differential equation $dY=f(Y)d\bm \om$ where $\bm \om=(ω,\bbomega)$ is a rough path defined by a Brownian motion on $\RR^m$. Under the usual regularity a…
Longtime behavior for 3D Navier-Stokes equations with constant delays
Hakima Bessaih, María J. Garrido-Atienza
This paper investigates the longtime behavior of delayed 3D Navier-Stokes equations in terms of attractors. The study will strongly rely on the investigation of the linearized Navi…
Setvalued dynamical systems for stochastic evolution equations driven by fractional noise
M. J. Garrido-Atienza, B. Schmalfuss, J. Valero
We consider Hilbert-valued evolution equations driven by Hölder paths with Hölder index greater than 1/2, which includes the case of fractional noises with Hurst parameters in (1/2…
Corrigendum to the chapter "Some aspects concerning the dynamics of stochastic chemostats"
Tomás Caraballo, María J. Garrido-Atienza, Javier López-de-la-Cruz +1
In this paper we correct an error made in a previous work, where a misleading stochastic system was obtained due to a lapse concerning a sign in one of the equations at the beginni…
On 3D Navier-Stokes equations: regularization and uniqueness by delays
Hakima Bessaih, María J. Garrido-Atienza, Björn Schmalfuss
A modified version of the three dimensional Navier-Stokes equations is considered with periodic boundary conditions. A bounded constant delay is introduced into the convective term…
Exponential stability of stochastic evolution equations driven by small fractional Brownian motion with Hurst parameter in
Luu Hoang Duc, María J. Garrido-Atienza, Andreas Neuenkirch +1
This paper addresses the exponential stability of the trivial solution of some types of evolution equations driven by Hölder continuous functions with Hölder index greater than $1/…
Stochastic lattice dynamical systems with fractional noise
Hakima Bessaih, María J. Garrido-Atienza, Xiaoying Han +1
This article is devoted to study stochastic lattice dynamical systems driven by a fractional Brownian motion with Hurst parameter . First of all, we investigate the ex…
Asymptotical stability of differential equations driven by Hölder--continuous paths
María J. Garrido-Atienza, Andreas Neuenkirch, Björn Schmalfuß
In this manuscript, we establish asymptotic local exponential stability of the trivial solution of differential equations driven by Hölder--continuous paths with Hölder exponent gr…
Random dynamical systems for stochastic evolution equations driven by multiplicative fractional Brownian noise with Hurst parameters
María J. Garrido-Atienza, Björn Schmalfuss, Kening Lu
We consider the stochastic evolution equation in a separable Hilbert--space . Here is supposed to be three times Fréchet--differentiable an…
Local pathwise solutions to stochastic evolution equations driven by fractional Brownian motions with Hurst parameters
María J. Garrido-Atienza, Kening Lu, Björn Schmalfuss
In this article we are concerned with the study of the existence and uniqueness of pathwise mild solutions to evolutions equations driven by a Hölder continuous function with Hölde…
Lévy-areas of Ornstein-Uhlenbeck processes in Hilbert-spaces
María J. Garrido-Atienza, Kening Lu, Björn Schmalfuss
In this paper we investigate the existence and some useful properties of the Lévy areas of Ornstein-Uhlenbeck processes associated to Hilbert-space-valued fractional Brownian-motio…
Stochastic Shell Models driven by a multiplicative fractional Brownian--motion
Hakima Bessaih, María J. Garrido-Atienza, Björn Schmalfuss
We prove existence and uniqueness of the solution of a stochastic shell--model. The equation is driven by an infinite dimensional fractional Brownian--motion with Hurst--parameter…
Random attractors for stochastic evolution equations driven by fractional Brownian motion
H. Gao, M. J. Garrido-Atienza, B. Schmalfuss
The main goal of this article is to prove the existence of a random attractor for a stochastic evolution equation driven by a fractional Brownian motion with . We wou…
Pathwise solutions of SPDEs driven by Hölder-continuous integrators with exponent larger than 1/2 and random dynamical systems
Y. Chen, H. Gao, M. J. Garrido-Atienza +1
This article is devoted to the existence and uniqueness of pathwise solutions to stochastic evolution equations, driven by a Hölder continuous function with Hölder exponent in $(1/…
Pathwise solutions and attractors for retarded SPDEs with time smooth diffusion coefficients
Hakima Bessaih, María J. Garrido-Atienza, Björn Schmalfuss
In this paper we study the longtime dynamics of mild solutions to retarded stochastic evolution systems driven by a Hilbert-valued Brownian motion. As a preparation for this purpos…
Pathwise solutions to stochastic partial differential equations driven by fractional Brownian motions with Hurst parameters in
María J. Garrido-Atienza, Kening Lu, Björn Schmalfuss
Combining fractional calculus and the Rough Path Theory we study the existence and uniqueness of mild solutions to evolutions equations driven by a Hölder continuous function with…