Zhao, Caidi; Zhou, Shengfan Sufficient conditions for the existence of global random attractors for stochastic lattice dynamical systems and applications. (English) Zbl 1192.37106 J. Math. Anal. Appl. 354, No. 1, 78-95 (2009). For random dynamical systems induced by stochastic lattice differential equations on \(l^2(\mathbb Z)\) with additive white noise a sufficient condition for the existence of a global random set attractor is given. As an application a ‘lattice sine-Gordon equation’ (i.e., a space discretization of a sine-Gordon equation) is discussed. For this case an upper bound for the \(\varepsilon\)-covering number, \(\varepsilon>0\), of the attractor is obtained in addition. Reviewer: Hans Crauel (Frankfurt) Cited in 54 Documents MSC: 37L55 Infinite-dimensional random dynamical systems; stochastic equations 37L60 Lattice dynamics and infinite-dimensional dissipative dynamical systems 60H99 Stochastic analysis Keywords:random set attractor; stochastic lattice dynamical system; asymptotic compactness; sine-Gordon equation; \(\varepsilon\)-covering number PDFBibTeX XMLCite \textit{C. Zhao} and \textit{S. Zhou}, J. Math. Anal. Appl. 354, No. 1, 78--95 (2009; Zbl 1192.37106) Full Text: DOI References: [1] Arnold, L., Random Dynamical Systems (1998), Springer: Springer Berlin [2] Bensoussan, A.; Temam, R., Equations stochastiques du type Navier-Stokes, J. Funct. Anal., 13, 195-222 (1973) · Zbl 0265.60094 [3] Bates, P. W.; Lu, K.; Wang, B., Attractors for lattice dynamical systems, Internat. J. Bifur. Chaos, 11, 143-153 (2001) · Zbl 1091.37515 [4] Bates, P. W.; Chen, X.; Chmaj, A., Traveling waves of bistable dynamics on a lattice, SIAM J. Math. 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