Abstract
In this paper, we first provide some sufficient conditions for the existence of global compact random attractors for general random dynamical systems in weighted space l ρ p ( p ⩾ 1 ) of infinite sequences. Then we consider the existence of global compact random attractors in weighted space l ρ 2 for stochastic lattice dynamical systems with random coupled coefficients and multiplicative/additive white noises. Our results recover many existing ones on the existence of global random attractors for stochastic lattice dynamical systems with multiplicative/additive white noises in regular l 2 space of infinite sequences.
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