María J. Garrido-Atienza

Stochastic stabilization of differential systems with general decay rate

Some sufficient conditions concerning stability of solutions of stochastic differential evolution equations with general decay rate are first proved. Then, these results are interpreted as suitable stabilization ones for deterministic and stochastic systems. Also, they permit us to construct appropriate linear stabilizers in some particular situations.

RANDOM ATTRACTORS FOR STOCHASTIC EQUATIONS DRIVEN BY A FRACTIONAL BROWNIAN MOTION

In this paper, the asymptotic behavior of stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/2 is studied. In particular, it is shown that the corresponding solutions generate a random dynamical system for which the existence and uniqueness of a random attractor is proved.

RANDOM DIFFERENTIAL EQUATIONS WITH RANDOM DELAYS

We investigate a random differential equation with random delay. First the non-autonomous case is considered. We show the existence and uniqueness of a solution that generates a cocycle. In particular, the existence of an attractor is proved. Secondly we look at the random case. We pay special attention to the measurability. This allows us to prove that the solution to the random differential equation generates a random dynamical system. The existence result of the attractor can be carried over to the random case.

Existence and uniqueness of solutions for delay stochastic evolution equations

Some results on the existence and uniqueness of solutions for stochastic evolution equations containing some hereditary characteristics are proved. In fact, our theory is developed from a variational point of view and in a general functional setting which permit us to deal with several kinds of delay terms in a unified formulation.

On the approximate controllability of a stochastic parabolic equation with a multiplicative noise

Abstract In this Note, we present some results concerning the approximate controllability for a stochastic parabolic equation with a multiplicative noise. For simplicity, we only consider the distributed control case.

Existence and uniqueness of solutions for delay evolution equations of second order in time

We prove some results on the existence and uniqueness of solutions for a class of evolution equations of second order in time, containing some hereditary characteristics. Our theory is developed from a variational point of view, and in a general functional setting which permits us to deal with several kinds of delay terms. In particular, we can consider terms which contain spatial partial derivatives with deviating arguments.

Random Attractors for Stochastic Evolution Equations Driven by Fractional Brownian Motion

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 Hurst parameter

Asymptotic Stability of Nonlinear Stochastic Evolution Equations

H\in (1/2,1)

Existence and Uniqueness of Solutions for Delay Stochastic Evolution Equations of Second Order in Time

. We would like to emphasize that we do not use the usual cohomology method, consisting of transforming the stochastic equation into a random one, but we deal directly with the stochastic equation. In particular, in order to get adequate a priori estimates of the solution needed for the existence of an absorbing ball, we will introduce stopping times to control the size of the noise. In the first part of this article we shall obtain the existence of a pullback attractor for the non-autonomous dynamical system generated by the pathwise mild solution of an nonlinear infinite-dimensional evolution equation with a nontrivial Holder continuous driving function. In the second part, we shall consider the random setup: stochastic equations having as a driving process a fractional Brownian motion with

STOCHASTIC POROUS MEDIA EQUATION DRIVEN BY FRACTIONAL BROWNIAN MOTION

H\in (1/2,1)