In this paper we give explicit representations for Kullback-Leibler information numbers between a priori and a posteriori distributions, when the observations come from a semimartingale. We assume that the distribution of the observed semimartingale is described in terms of the so-called triplet of predictable characteristics. We end by considering the corresponding notions in a model with a fractional noise.

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CWI. Probability, Networks and Algorithms [PNA]
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Dzhaparidze, K.O, Spreij, P.J.C, & Valkeila, E. (2001). Information processes in filtered experiments. CWI. Probability, Networks and Algorithms [PNA]. CWI.