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Effective Filtering Analysis for Non-Gaussian Dynamic Systems

  • Yanjie Zhang
  • Huijie QiaoEmail author
  • Jinqiao Duan
Article
  • 30 Downloads

Abstract

This work is about a slow-fast data assimilation system under non-Gaussian noisy fluctuations. Firstly, we show the existence of a random invariant manifold for a stochastic dynamical system with non-Gaussian noise and two-time scales. Secondly, we obtain a low dimensional reduction of this system via a random invariant manifold. Thirdly, we prove that the low dimensional filter on the random invariant manifold approximates the original filter, in a probabilistic sense.

Keywords

Random invariant manifold \(\alpha \)-Stable noise Zakai equation Data assimilation Non-Gaussian noise 

Mathematics Subject Classification

60H10 37D10 70K70 

Notes

Acknowledgements

We would like to thank Xianming Liu (Huazhong University of Sciences and Technology, China) for helpful discussions.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of MathematicsSouth China University of TechnologyGuangzhouChina
  2. 2.School of MathematicsSoutheast UniversityNanjingChina
  3. 3.Department of Applied MathematicsIllinois Institute of TechnologyChicagoUSA

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