Dynamical inference for transitions in stochastic systems with α-stable Lévy noise

Ting Gao, Jinqiao Duan, Xingye Kan, Zhuan Cheng

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


A goal of data assimilation is to infer stochastic dynamical behaviors with available observations. We consider transition phenomena between metastable states for a stochastic system with (non-Gaussian) α;-stable Lévy noise. With either discrete time or continuous time observations, we infer such transitions between metastable states by computing the corresponding non-local Zakai equation (and its discrete time counterpart) and examining the most probable orbits for the state system. Examples are presented to demonstrate this approach.

Original languageEnglish (US)
Article number294002
JournalJournal of Physics A: Mathematical and Theoretical
Issue number29
StatePublished - Jun 10 2016
Externally publishedYes

Bibliographical note

Funding Information:
This work was partly supported by the NSF Grant 1025422.

Publisher Copyright:
© 2016 IOP Publishing Ltd.


  • mean exit time with observation
  • most probable orbits
  • non-local Laplace operator
  • non-local Zakai equation
  • transitions between metastable states


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