The work is about multiscale stochastic dynamical systems driven by Lévy processes. We prove that such a system can be approximated by a low-dimensional system on a random invariant manifold, and the original filter can be also approximated by the reduced low-dimensional filter. Finally, we investigate the reduction for \(\varepsilon =0\) and obtain that these reduced systems does not approximate these multiscale stochastic dynamical systems.

中文翻译：

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Lévy过程驱动的多尺度随机动力系统的有效过滤*

这项工作是关于由Lévy过程驱动的多尺度随机动力学系统。我们证明了这样的系统可以由随机不变流形上的低维系统近似，并且原始滤波器也可以由简化的低维滤波器近似。最后，我们研究\（\ varepsilon = 0 \）的约简，并获得这些约简的系统不近似于这些多尺度随机动力学系统。