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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

Citations:

Zbl 0462.60048
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