Note on randomized filtered experiments in presence of nuisance parameters

In this report we define randomized filtered experiments with an abstract parameter space consisting not only parameters of interest but also nuisance parameters. The generalized Hellinger process, introduced in cite{dsv to characterize the experiment, is shown to decompose in two components associated separately with the set of parameters of interest and with the set of nuisance parameters. Explicit expressions are presented for these characteristics in the case of general semimartingale observations and in the case of multivariate counting processes.