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We consider a nonlinear filtering problem of multiscale non-Gaussian signal processes and observation processes with jumps. First, we prove that the dimension for the signal system can be reduced by a homogenized approach. Second, convergence of the corresponding nonlinear filtering to the homogenized filtering is shown by a weak convergence technique. Finally, we give an example to explain our result.

Convergence of nonlinear filterings for stochastic dynamical systems with Lévy noises