快慢随机微分系统的慢流形与平均
Slow manifold and averaging for slow-fast stochastic differential system
摘要：
我们考虑多尺度随机动力系统。本文针对白噪声驱动的快模慢-快系统，给出了一个\emph{intermediate}简化模型。首先将指数吸引慢流形约化系统的约化随机系统导出为$\mathcal{O}(ε)$的误差。第二，求平均得到一个直到误差为$\mathcal{O}(\sqrtε)$的自治确定性系统。然后，使用鞅方法推导出一个中间简化模型，该模型是一个由白噪声驱动的自治确定性系统，误差高达$\mathcal{O}(ε)$，以解释平均系统的波动。该中间约化模型比随机慢流形上的约化模型具有更简单的形式。
英文摘要：
We consider multiscale stochastic dynamical systems. In this article an \emph{intermediate} reduced model is obtained for a slow-fast system with fast mode driven by white noise. First, the reduced stochastic system on exponentially attracting slow manifold reduced system is derived to errors of $\mathcal{O}(ε)$. Second, averaging derives an autonomous deterministic system up to errors of $\mathcal{O}(\sqrtε)$. Then an intermediate reduced model, which is an autonomous deterministic system driven by white noise up to errors of $\mathcal{O}(ε)$, is derived using a martingale approach to account for fluctuations about the averaged system. This intermediate reduced model has a simpler form than the reduced model on the stochastic slow manifold.
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