Information-equivalence: On Filtrations Created by Independent Increments

Abstract

This article investigates filtrations created by the increments-processes of processes with independent increments: Suppose two processes create the same filtrations, when will the processes of their increments also create the same filtrations?

Our main result is that the processes of increments of two extremal continuous martingales with independent increments create the same filtrations if and only if either process admits a deterministic representation with respect to the other.