GARRIDO ATIENZA , María José

In this paper we investigate the existence, uniqueness and exponential asymptotic behavior of mild solutions to stochastic delay evolution equations perturbed by a fractional Brownian motion BH Q (t): dX(t) = (AX(t) + f(t;Xt))dt + g(t)dBH Q (t); with Hurst parameter H 2 (1=2; 1). We also consider the existence of weak solutions.

We consider the exponential stability of semilinear stochastic evolution equations with delays when zero is not a solution for these equations. We prove the existence of a non-trivial stationary solution exponentially stable, for which we use a general random fixed point theorem for general cocycles. We also construct stationary solutions with...

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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...

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.

Sufficient conditions for exponential mean square stability of solutions to delayed stochastic partial differential equations of second order in time are established. As a consequence of these results, some ones on the pathwise exponential stability of the system are proved. The stability results derived are applied also to partial differential...

Sufficient conditions for exponential mean square stability of solutions to delayed stochastic partial differential equations of second order in time are established. As a consequence of these results, the pathwise exponential stability of the system is also deduced. The stability results derived can be applied also to partial differential...

Some results on the pathwise asymptotic stability of solutions to stochastic partial differential equations are proved. Special attention is paid in proving sufficient conditions ensuring almost sure asymptotic stability with a nonexponential decay rate. The situation containing some hereditary characteristics is also treated. The results are...

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.