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In this paper we study progressive filtration expansions with cadlagprocesses. Using results from the weak convergence of sigma fields theory, wefirst establish a semimartingale convergence theorem. Then we apply it in afiltration expansion with a process setting and provide sufficient conditionsfor a semimartingale of the base filtration to remain a semimartingale in theexpanded filtration. Finally, an application to the expansion of a Brownianfiltration with a time reversed diffusion is given through a detailed study.

On progressive filtration expansion with a process