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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The author would like to thank the anonymous referee for valuable comments and suggestions which led to a big improvement of the presentation of the paper.
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This work was supported by NSF of China (No. 11001051, 11371352, 12071071) and China Scholarship Council under Grant No. 201906095034.
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Qiao, H. Effective Filtering for Multiscale Stochastic Dynamical Systems Driven by Lévy Processes*. J Dyn Diff Equat 34, 2491–2509 (2022). https://doi.org/10.1007/s10884-021-09981-5
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DOI: https://doi.org/10.1007/s10884-021-09981-5
Keywords
- Multiscale systems driven by Lévy processes
- Random slow manifolds
- Dimension reduction
- Efficient filtering