Before revision:  The proposed approach is based on Information Theory  and relies on the quantification of information loss due to parameter perturbations between time-series distributions , hence referred to as "pathwise".
After revision:  The proposed approach is based on Information Theory and relies on the quantification of information loss due to parameter perturbations between time-series distributions . For this reason, we need to work on path-space, i.e., the set consisting of all stochastic trajectories, hence the proposed approach is referred to as "pathwise".