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Zbl 0719.60087
Malric, Marc
Filtrations browniennes et balayage. (Brownian filtrations and balayage). (French)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 26, No.4, 507-539 (1990). ISSN 0246-0203

Let $(X\sb t)\sb{t\ge 0}$ be an n-dimensional Brownian motion and A an $n\times n$ real matrix. This paper studies the natural filtration of the process $M\sp A\sb t=\int\sp{t}\sb{0}(AX\sb s,dX\sb s)$, $t\ge 0$. The author investigates the cases where this filtration is that of a k- dimensional Brownian motion, for some integer k. Extending the results of {\it J. Auerhan} and {\it 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 $n\le 3$. The proof uses the Azéma-Yor ``balayage'' formula for semi-martingales and quadratic Brownian filtrations.
[M.Chaleyat-Maurel (Paris)]

MSC 2000:: *60J65 Brownian motion
60J55 Additive functionals
60H05 Stochastic integrals
60G44 Martingales with continuous parameter

Keywords: Brownian motion; balayage; semi-martingales; quadratic Brownian filtrations

Citations: Zbl 0462.60048

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