Exponentially Stable Stationary Solutions for Stochastic Evolution Equations and Their Perturbation

238 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Stabilization by noise for a class of stochastic reaction-diffusion equations (2005, background): “[1], [2], [18] and [19]; see also [3], [4], [12] and [15] for some results in infinite dimension).”
Pathwise Random Periodic Solutions of Stochastic Differential Equations (2011, background): “ a stationary solution or a random periodic solution or has more complicated topology is a basic problem. In fact, for the existence of stationary solutions, results are only known in very few cases ([3],[6],[17],[24],[25],[28]). Even for the stationary solution case, researchers can only construct ”
Smooth Stable and Unstable Manifolds for Stochastic Evolutionary Equations (2004, background): “l measure t → u∗(θtω) is a solution version for (13). It will not be the topic of this article to deal with stationary solutions. For the existence of stable stationary solutions see Caraballo et al. [5]. We now deﬁne the nonlinear operator G(ω,x) = F(x +u∗(ω)) −F(u∗(ω)). Note that G has the same Li”
Invariant Manifolds for Random and Stochastic Partial Differential Equations (2009, background): “5.37) for some ν > 0. This equation has a random ﬁxed point in the sense of random dynamical systems generating a stationary solution known as the stationary Ornstein-Uhlenbeck process. Lemma 5.1 ([7]) Let νbe a positive number and consider the probability space as in Section 2. There exists a {θ”