带可乘白噪声的Schr(o)dinger格点系统的随机吸引子

摘要

主要考虑带可乘白噪声的随机Schr(o)dinger格点系统的随机吸引子的存在性.首先,利用Ornstein-Uhlenbeck过程将具白噪声的随机Schr(o)dinger格点系统转化成以随机变量为系数而无噪声的随机格点系统;其次,研究该随机系统的初值问题的整体解的存在唯一性,其解映射可以生成随机动力系统;最后,证明该随机动力系统的有界随机吸收集和随机吸引子的存在性.%It was mainly studied the existence of a random attractor for stochastic Schr(o)dinger lattice system.Firstly,the stochastic Schr(o)dinger lattice system with multiplicative white noise was transferred into a random dynamical system with random coefficients and without noise by the Ornstein-Uhlenbeck process.Secondly,the existence and uniqueness of solution for lattice system with initial condition were considered,and mapping of this solution generated a random dynamical system.Finally,the problem of the existence of a random bounded absorbing set and a random attractor were also investigated.