  In this paper we study progressive filtration expansions with cadlag
processes. Using results from the weak convergence of sigma fields theory, we
first establish a semimartingale convergence theorem. Then we apply it in a
filtration expansion with a process setting and provide sufficient conditions
for a semimartingale of the base filtration to remain a semimartingale in the
expanded filtration. Finally, an application to the expansion of a Brownian
filtration with a time reversed diffusion is given through a detailed study.
