In this paper, we prove the existence of local stable and unstable invariant manifolds for a class of random differential equations driven by nonlinear colored noise defined in a fractional power of a separable Banach space. In the case of linear noise, we show the pathwise convergence of these random invariant manifolds as well as invariant foliations as the correlation time of the colored noise approaches zero.

中文翻译：

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有色噪声驱动的随机微分方程的不变流形和叶型

在本文中，我们证明了由一类可分的Banach空间的分数次幂定义的非线性有色噪声驱动的一类随机微分方程的局部稳定和不稳定不变流形的存在。在线性噪声的情况下，当有色噪声的相关时间接近零时，我们显示了这些随机不变流形以及不变叶的路径收敛。