Metrics on the set of semimartingale filtrations

摘要

Let X be a stochastic process with cadlag paths. We consider the set of all filtrations under which X is a semimartingale, and we define a distance between such filtrations with the help of the bounded variation parts in the corresponding decompositions of X. We show that this distance is a complete metric on the set of semimartingale filtrations if the given process X is continuous.