An averaging principle for filtering a jump process with point process observations

A proof of the following result is given. Le X/sub t/ and Y/sub t/ be two jump processes which modulate the intensity of a multivariate point process N/sub t/, and suppose that the process X/sub t/ is a fast' Markov chain with a unique invariant probability distribution. Then the filtering equations for Y/sub t/ can be obtained by considering, instead of the original problem, the averaged problem where the intensity is replaced by the averaged intensity.<
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