Wong-Zakai approximations and random attractors for nonlocal stochastic Schrödinger lattice systems in weighted spaces

This paper deals with the long-term behavior of nonlocal Schrödinger lattice systems with multiplicative white noise and their Wong-Zakai approximate systems in weighted spaces. We first prove the existence and uniqueness of tempered pullback attractors for the original stochastic systems and the Wong-Zakai approximations. Then, we establish the upper semicontinuity of these attractors for the Wong-Zakai approximate systems as the step length of the Wiener shift approaches zero.