Random exponential attractor for a class of non-autonomous stochastic lattice systems

The purpose of this paper was to discuss the existence of a random exponential attractor for non-autonomous coupled Klein-Gordon-Schrödinger (KGS) lattice equations with multiplicative noise. We employed the method of estimation on the tails of solutions to prove the existence of a random attractor for a continuous cocycle generated by the random KGS lattice equations on an infinite-dimensional sequence space, and used this abstract result to prove the Lipschitz continuity of the continuous cocycle. Then, we verified the existence of a random exponential attractor for the investigated system according to a known criterion.