We prove the existence of a random exponential attractor for a non-autonomous Zakharov lattice system with multiplicative white noise. We first transfer the stochastic lattice system into an equivalent random lattice system whose solutions generate a continuous cocycle on a phase space of infinite sequences. Then we estimate the tail of solutions for the random system. We next verify that the continuous cocycle satisfies the Lipschitz continuity and the random squeezing property on a tempered random closed absorbing set. Finally, we check the boundedness of the expectation of some random variables and obtain the existence of a random exponential attractor.

我们证明了具有乘法白噪声的非自治 Zakharov 格系统的随机指数吸引子的存在。我们首先将随机晶格系统转换为等效的随机晶格系统，其解在无限序列的相空间上生成连续的共循环。然后我们估计随机系统的解尾。我们接下来验证连续共环满足 Lipschitz 连续性和在调和随机闭合吸收集上的随机挤压特性。最后，我们检查一些随机变量的期望的有界性，并获得随机指数吸引子的存在性。