## Brownian filtrations and balayage. (Filtrations browniennes et balayage.)(French)Zbl 0719.60087

Let $$(X_t)_{t\geq 0}$$ be an $$n$$-dimensional Brownian motion and $$A$$ an $$n\times n$$ real matrix. This paper studies the natural filtration of the process $$M^A_t = \int^t_0 (AX_s,dX_s)$$, $$t\geq 0$$. The author investigates the cases where this filtration is that of a $$k$$-dimensional Brownian motion, for some integer $$k$$. Extending the results of J. Auerhan and D. Lépingle [Séminaire de probabilités XV, Univ. Strasbourg 1979/80, Lect. Notes Math. 850, 643–668 (1981; Zbl 0462.60048)], he proves the result for $$n\leq 3$$. The proof uses the Azéma-Yor “balayage” formula for semi-martingales and quadratic Brownian filtrations.

### MSC:

 60J65 Brownian motion 60J55 Local time and additive functionals 60H05 Stochastic integrals 60G44 Martingales with continuous parameter

Zbl 0462.60048
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