Doob’s Maximal Identity, Multiplicative Decompositions and Enlargements of Filtrations
نویسنده
چکیده
In the theory of progressive enlargements of filtrations, the supermartingale Zt = P (g > t | Ft) associated with an honest time g, and its additive (Doob-Meyer) decomposition, play an essential role. In this paper, we propose an alternative approach, using a multiplicative representation for the supermartingale Zt, based on Doob’s maximal identity. We thus give new examples of progressive enlargements. Moreover, we give, in our setting, a proof of the decomposition formula for martingales , using initial enlargement techniques, and use it to obtain some path decompositions given the maximum or minimum of some processes.
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