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

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1 Author(s)
Bremaud, P. ; Ecole Superieure d''Electr., Gif-sur-Yvette, France

A proof of the following result is given. Le Xt and Yt be two jump processes which modulate the intensity of a multivariate point process N t, and suppose that the process Xt is a fast' Markov chain with a unique invariant probability distribution. Then the filtering equations for Yt 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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Information Theory, IEEE Transactions on  (Volume:34 ,  Issue: 3 )