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We consider parametric estimation for ergodic diffusion processes with noisy sampled data based on the hybrid method, that is, the multi-step estimation with the initial Bayes type estimators in order to select proper initial values for optimisation of the quasi likelihood function. The asymptotic properties of the initial Bayes type estimators and the hybrid multi-step estimators are shown, and a concrete example and the simulation results are given.

Hybrid estimation for ergodic diffusion processes based on noisy discrete observations