Random Attractor For Schr(?)dinger Lattice System With Multiplicative White Noise

In this article,we mainly study the existence of a random attractor for stochastic Schr(?)dinger lattice system with multiplicative white noise and random coupled coeffi-cients.This article consists of three chapters.In the first chapter,we first introduce the background of the problem and research status of infinite dimensional dynamical system.Then we introduces the relevant knowl-edge,including basic concepts,theorems and the required inequality.Lastly,we introduce the main results of this paper.The second chapter and the third chapter are the main part of this paper,we show that a random attractor of autonomous Schr(?)dinger lattice system with multiplicative white noise and a random attractor of non-autonomous Schr(?)dinger lattice system with random coupling coefficients and multiplicative white noise system.In the process of proof,we first transfer the stochastic Schr(?)dinger lattice system into a random dynamical system with random coefficients and without noise by the Ornstein-Uhlenbeck process.Secondly,we consider the existence and uniqueness of solution for lattice system with initial condition,and mapping of this solution can generate a random dynamical system.Finally,we study the problem of the existence of a random bounded absorbing set and a random attractor.