  In this paper we study progressive filtration expansions with random times.
We show how semimartingale decompositions in the expanded filtration can be
obtained using a natural link between progressive and initial expansions. The
link is, on an intuitive level, that the two coincide after the random time. We
make this idea precise and use it to establish known and new results in the
case of expansion with a single random time. The methods are then extended to
the multiple time case, without any restrictions on the ordering of the
individual times. Finally we study the link between the expanded filtrations
from the point of view of filtration shrinkage. As the main analysis
progresses, we indicate how the techniques can be generalized to other types of
expansions.
