On progressive filtration expansion with a process

Details On progressive filtration expansion with a process On progressive filtration expansion with a process

2011-05-09

arxiv.org/abs/1105.1662v1

Mathematics

Probability

Scientific paper

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.

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