带可乘白噪声的Schrdinger格点系统的随机吸引子

Random attractor for Schrdinger lattice system with multiplicative white noise

主要考虑带可乘白噪声的随机Schr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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 Schrodinger lattice system. Firstly, the stochastic Schrodinger lattice system with muhiplicative white noise was transfered 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.