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Abstract
In this paper, we first present some sufficient conditions for the existence of random attractors for general continuous random dynamical systems (RDSs) defined on the separable Banach space consisting of continuous functions from
(
) into the weighted space
of infinite sequences and continuous RDSs associated with stochastic retarded lattice dynamical systems in the state space
, where
is a positive-valued function from
into
and
is a positive constant. Then we apply the obtained abstract result to the first-order stochastic retarded lattice system with random coupled coefficients and additive white noise.
Acknowledgements
The authors would like to express their sincere thanks to the anonymous referees for their time and useful suggestions and comments, which led to a much improved quality of this work. This work was supported by National Natural Science Foundation of China under Grant 11071165, 61271396 and Zhejiang Normal University (ZC304011068).