Random Second-order Stochastic Lattice Systems With Random Coupling Coefficient Attractors

In this paper, we mainly focus on the asymptotic behavior of solutions to the second-orderstochastic lattice equations with random coupled coefficients and multiplicative white noise inweighted space of infinite sequences. We first transfer the stochastic lattice equations into arandom lattice equations and prove the existence and uniqueness of solutions which generate arandom dynamical system. Second we consider the existence of tempered random bounded ab-sorbing set and a random attractor for the system. Then we establish the upper semicontinuity ofrandom attractors as the coefficient of the white noise term tends to zero. Finally we present thecorresponding results for the system with additive white noises.