Abstract
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.
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