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Random attractors for stochastic retarded lattice systems. (English) Zbl 1309.37074

Summary: 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 \(C([-\nu,0],l^p_\rho)\) consisting of continuous functions from \([-\nu,0](\nu>0)\) into the weighted space \(l^p_\rho(p\geq1)\) of infinite sequences and continuous RDSs associated with stochastic retarded lattice dynamical systems in the state space \(C([-\nu,0],l^p_\rho)\), where \(\rho\) is a positive-valued function from \(\mathbb Z\) into \((0,M_0]\subset\mathbb R^+\) and \(M_0\) 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.

MSC:

37L55 Infinite-dimensional random dynamical systems; stochastic equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35B41 Attractors
35R60 PDEs with randomness, stochastic partial differential equations
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