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The theory of random attractors has different notions of attraction, amongst them pullback attraction and weak attraction. We investigate necessary and sufficient conditions for the existence of pullback attractors as well as of weak attractors.
We study pullback attractors of non-autonomous non-compact dynamical systems generated by differential equations with non-autonomous deterministic as well as stochastic forcing terms. We first introduce the concepts of pullback attractors and asympto
The upper semicontinuity of random attractors for non-compact random dynamical systems is proved when the union of all perturbed random attractors is precompact with probability one. This result is applied to the stochastic Reaction-Diffusion with white noise defined on the entire space R^n.
We consider random walks in i.i.d. elliptic random environments which are not uniformly elliptic. We introduce a computable condition in dimension $d=2$ and a general condition valid for dimensions $dge 2$ expressed in terms of the exit time from a b
The existence of a random attractor for the stochastic FitzHugh-Nagumo system defined on an unbounded domain is established. The pullback asymptotic compactness of the stochastic system is proved by uniform estimates on solutions for large space and
This paper is concerned with the asymptotic behavior of solutions of the two-dimensional Navier-Stokes equations with both non-autonomous deterministic and stochastic terms defined on unbounded domains. We first introduce a continuous cocycle for the