The exponential \(e^{\Lambda t}\) of the lattice Laplacian operator \(\Lambda \) was introduced in the 1970 s, but, unlike its counterpart for parabolic partial differential equations, has not yet been used to investigate lattice dynamical systems. Here its properties are investigated in the weighted sequence space \(\ell _{\rho }^2\) . Then it is used to formulate and to establish the existence and uniqueness of mean-square solutions of a nonlocal stochastic lattice system with coefficient functions depending on the expectation of the solution. Finally, it is used to show that the mean-square random dynamical system so generated possesses a mean-square random attractor.
