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We consider the problem of estimating the state of a continuous-time Markovchain from noisy observations. We show that the corresponding optimal filter isstrictly contracting pathwise, when considered in the Hilbert projective space,and give explicit deterministic and pathwise rates of convergence. Using this,we provide alternative proofs of the robustness of optimal filters, improvingon known error estimates, and derive rigorous and computable error bounds forapproximate filters.

Exponential contractions and robustness for approximate Wonham filters