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Let Z=(X, Y) be a planar brownian motion, the filtration it generates, andBa linear brownian motion in the filtration . One says thatB(or its filtration) is maximal if no other linear -brownian motion has a filtration strictly bigger than that ofB. For instance, it is shown in [In Séminaire de Probabilités XLI 265–278 (2008) Springer] that B is maximal if there exists a linear brownian motion C independent of B and such that the planar brownian motion (B, C) generates the same filtration asZ....
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