Intégrales stochastiques de processus anticipants et projections duales prévisibles.
Donati-Martin, Catherine ; Yor, Marc
Publicacions Matemàtiques, Tome 43 (1999), p. 281-301 / Harvested from Biblioteca Digital de Matemáticas
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We define a stochastic anticipating integral δμ with respect to Brownian motion, associated to a non adapted increasing process (μt), with dual projection t. The integral δμ(u) of an anticipating process (ut) satisfies: for every bounded predictable process ft,

E [ (∫ fsdBs ) δμ(u) ] = E [ ∫ fsusdμs ].

We characterize this integral when μt = supt ≤s ≤ 1 Bs. The proof relies on a path decomposition of Brownian motion up to time 1.

Publié le : 1999-01-01
DMLE-ID : 3888 
@article{urn:eudml:doc:41359,
     title = {Int\'egrales stochastiques de processus anticipants et projections duales pr\'evisibles.},
     journal = {Publicacions Matem\`atiques},
     volume = {43},
     year = {1999},
     pages = {281-301},
     mrnumber = {MR1697526},
     zbl = {0936.60051},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41359}
}

Donati-Martin, Catherine; Yor, Marc. Intégrales stochastiques de processus anticipants et projections duales prévisibles.. Publicacions Matemàtiques, Tome 43 (1999) pp. 281-301. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41359/