Random uniform exponential attractors for non-autonomous stochastic Schr o?dinger lattice systems in weighted space

We mainly study the existence of random uniform exponential attractors for non -autonomous stochastic Schr delta dinger lattice system with multiplicative white noise and quasi-periodic forces in weighted spaces. Firstly, the stochastic Schr delta dinger system is transformed into a random system without white noise by the Ornstein-Uhlenbeck process, whose solution generates a jointly continuous non-autonomous random dynamical system phi. Secondly, we prove the existence of a uniform absorbing random set for phi in weighted spaces. Finally, we obtain the existence of a random uniform exponential attractor for the considered system phi in weighted space.