: 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 discussedNature: Original Retrieve article from Numdam