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Random attractors for stochastic lattice dynamical systems in weighted spaces. (English) Zbl 1208.60063
Summary: We first provide some sufficient conditions for the existence of global compact random attractors for general random dynamical systems in weighted space $$l_{\rho}^p (p \geqslant 1)$$ of infinite sequences. Then we consider the existence of global compact random attractors in weighted space $$l_{\rho}^2$$ 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.

##### MSC:
 60H15 Stochastic partial differential equations (aspects of stochastic analysis)
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