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In the first part the natural filtration of an Rd-valued Brownian motion B is compared to that of the BM $$ B\prime = \int_0^ \cdot {HdB} $$ , where H is previsible in the filtration of B and valued in Od(R). We show that there exists a r.v. U, independent of B′ and uniformly distributed on [0, 1] or on some finite set, such...
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