中文摘要：

主要研究了定义在无界区域上具可乘白噪音的Fitzhugh—Nagumo方程的渐近行为．首先运用Ornstein-Uhlenbeck变换，将Fitzhugh—Nagumo方程转换成带有随机参数的确定型系统，并生成了相应的随机动力系统．其次运用一致估计证明了所生成的随机动力系统的渐近性．最后，证明了该随机动力系统的随机吸引子的存在性．

英文摘要：

This paper is devoted to investigating the asymptotic behavior for Fitzhugh-Nagumo systems with multiplicative white noise on unbounded domains. Firstly, by using Ornstein-Uhlenbeck transformation, the Fitzhugh-Nagumo systems are transferred into a deterministic case with random parameter and generate the corresponding random dynamical system. Secondly, applying the uniform priori estimates to solutions, we prove the asymptotic compactness of the mentioned random dynamical system. Finally, the existence of a random attractor for this random dynamical system is established.