Quotient filtrations of Brownian filtration. (Filtrations quotients de la filtration brownienne.) (French) Zbl 0979.60070

Azéma, Jacques (ed.) et al., Séminaire de Probabilités XXXV. Berlin: Springer. Lect. Notes Math. 1755, 260-264 (2001).
The main result of this paper is the following: If \({\mathcal F}\) is a (canonical) Brownian filtration of dimension \(d\) and \(\Gamma\) any subgroup of \({\mathbf O} (d)\), then the quotient filtration \({\mathcal F}/\Gamma\) (which is obtained through the natural equivalence relation associated with \(\Gamma\) on the Wiener space) is a Brownian filtration immerged in \({\mathcal F}\). This generalizes a result of A. Goswami and B. V. Rao [Stochastics Stochastics Rep. 35, No. 4, 213-214 (1991; Zbl 0728.60059)].
For the entire collection see [Zbl 0960.00020].


60J65 Brownian motion


Zbl 0728.60059
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