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.
"Information processes for semimartingale experiments." Ann. Probab. 31 (1) 216 - 243, January 2003. https://doi.org/10.1214/aop/1046294310