XIV: 22, 200-204, LNM 784 (1980)
AUERHAN, J.;
LÉPINGLE, Dominique;
YOR, Marc
Construction d'une martingale réelle continue de filtration naturelle donnée (
General theory of processes)
It is proved in
1123 that, under a mere separability assumption, any filtration is the natural filtration of some bounded left-continuous increasing process $(A_t)$. If the filtration contains a Brownian motion $(B_t)$, then it is also the natural filtration of the continuous martingale $\int_0^t A_sdB_s$. Therefore, the natural filtration of (finitely or countably) many independent Brownian motions is generated by a single continuous martingale. Explicit constructions are discussed
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