Abstract
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.
Citation
Huijie Qiao. Jinqiao Duan. "Nonlinear filtering of stochastic dynamical systems with Lévy noises." Adv. in Appl. Probab. 47 (3) 902 - 918, September 2015. https://doi.org/10.1239/aap/1444308887
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