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Artículo
Exponentially Stable Stationary Solutions for Stochastic Evolution Equations and Their Perturbation
(2004)
We consider the exponential stability of stochastic evolution equations with Lipschitz continuous non-linearities when zero is not a solution for these equations. We prove the existence of a non-trivial stationary solution ...
Artículo
Stabilization of Stationary Solutions of Evolution Equations by Noise
(2006)
We investigate the existence, uniqueness and exponential stability of non-constant stationary solutions of stochastic semilinear evolution equations. Our main result shows, in particular, that noise can have a stabilization ...
Artículo
The pathwise numerical approximation of stationary solutions of semilinear stochastic evolution equations
(2006)
Under a one-sided dissipative Lipschitz condition on its drift, a stochastic evolution equation with additive noise of the reaction-diffusion type is shown to have a unique stochastic stationary solution which pathwise ...