随机时滞Schrodinger格系统的不变测度

Invariant measures of stochastic Schrodinger delay lattice systems

本文研究随机时滞Schrodinger格系统,其漂移和扩散系数是局部Lipschitz连续的.首先,建立一些解的一致估计,包括高阶矩估计和一致尾端估计.其次,运用Arzelà-Ascoli定理和二分法技巧证明解的概率分布族在空间C([-ρ,0];l^(2))中的胎紧性.最后,利用Krylov-Bogolyubov方法证明系统Markov半群不变测度的存在性.

In this paper,we investigate stochastic Schrodinger lattice systems with time delay,whose drift and diffusion coefficients are locally Lipschitz continuous.Firstly,some uniform estimates of solutions are established,which include higher-order moment estimates and uniform tail-estimates.Then the tightness of a family of probability distributions of solutions in C([-ρ,0];l^(2))is proved by the Arzelà-Ascoli theorem and the technique of diadic division.Finally,the existence of invariant measures for the Markov semigroup of the system is proved by the Krylov-Bogolyubov method.