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Attractors for stochastic lattice dynamical systems. (English) Zbl 1105.60041
For dynamical systems described by infinite-dimensional stochastic differential equations (SDEs) on a one-dimensional lattice, stability and existence of random attractors are established. The class of SDE systems under consideration is characterised by independent additive Wiener processes in each component, dissipation terms, nonlinearity which also helps dissipation, and diffusive type interaction between neighbour particles via discrete Laplace operator. For such SDE systems, existence, uniqueness, continuous dependence on initial data, and a priori bounds for solutions have been proved. Existence of a unique compact global random attractor in the class of tempered sets is established.

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