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We define a stochastic anticipating integral  µ with respect to Brownian motion, associated to a non adapted increasing process (µt ), with dual projection t. The integral  µ (u) of an anticipating process (ut ) satisfies: for every bounded predictable process. We characterize this integral when µt = supts1 Bs . The proof relies on a path decomposition of Brownian motion up to time 1

Intégrales stochastiques de processus anticipants et projections duales prévisibles