Effective Filtering Analysis for Non-Gaussian Dynamic Systems

  • Yanjie Zhang
  • Huijie QiaoEmail author
  • Jinqiao Duan


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.


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

Mathematics Subject Classification

60H10 37D10 70K70 



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


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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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