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3 results

  • Nonlinear filtering of stochastic dynamical systems with Lévy noises

  • Part of
  • Huijie Qiao, Jinqiao Duan
  • Journal:
    Advances in Applied Probability / Volume 47 / Issue 3 / September 2015
    Published online by Cambridge University Press:
    21 March 2016, pp. 902-918
    Print publication:
    September 2015
    • Article
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  • Nonlinear filtering is investigated in a system where both the signal system and the observation system are under non-Gaussian Lévy fluctuations. Firstly, the Zakai equation is derived, and it is further used to derive the Kushner-Stratonovich equation. Secondly, by a filtered martingale problem, uniqueness for strong solutions of the Kushner-Stratonovich equation and the Zakai equation is proved. Thirdly, under some extra regularity conditions, the Zakai equation for the unnormalized density is also derived in the case of α-stable Lévy noise.