Data assimilation and parameter estimation for a multiscale stochastic system with α-stable Lévy noise**This work was partly supported by the NSF grant 1620449, and NSFC grants 11531006, 11371367, and 11271290.

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This work is about low dimensional reduction for a slow-fast data assimilation system with non-Gaussian stable Lévy noise via stochastic averaging. When the observations are only available for slow components, we show that the averaged, low dimensional filter approximates the original filter, by examining the corresponding Zakai stochastic partial differential equations. Furthermore, we demonstrate that the low dimensional slow system approximates the slow dynamics of the original system, by examining parameter estimation and most probable paths.