论文标题
在希尔伯特空间中随机演化方程慢速系统的平均原理中的收敛顺序
The order of convergence in the averaging principle for slow-fast systems of stochastic evolution equations in Hilbert spaces
论文作者
论文摘要
在这项工作中，我们关注的是对具有加性噪声的希尔伯特空间中随机进化方程的缓慢快速系统的平均原理中强大的收敛顺序的研究。特别是随机扰动是一般维也纳过程，即它们的协方差操作员被允许不为跟踪类。我们证明，缓慢的组件与融合$ 1/2 $的平均汇合均强烈收敛，这是最佳的。此外，我们将此结果应用于缓慢的随机反应扩散系统，在时间和空间中，随机扰动都通过白噪声给出。
In this work we are concerned with the study of the strong order of convergence in the averaging principle for slow-fast systems of stochastic evolution equations in Hilbert spaces with additive noise. In particular the stochastic perturbations are general Wiener processes, i.e their covariance operators are allowed to be not trace class. We prove that the slow component converges strongly to the averaged one with order of convergence $1/2$ which is known to be optimal. Moreover we apply this result to a slow-fast stochastic reaction diffusion system where the stochastic perturbation is given by a white noise both in time and space.
