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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

Nature: Original

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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

Nature: Original

Retrieve article from Numdam