On a theorem of Tsirelson with respect to correlated Brownian motion and zeros of local terms. (Sur un théorème de Tsirelson relatif à des mouvements browniens corrélés et à la nullité de certains temps locaux.) (French) Zbl 0949.60088

Azéma, Jacques (ed.) et al., Séminaire de probabilités XXXII. Berlin: Springer. Lect. Notes Math. 1686, 306-312 (1998).
The authors give a new proof, based on classical stochastic calculus, of one of the big lemmas involved in B. Tsirelson’s famous theorem stating that Walsh’s filtrations are not Brownian [Geom. Funct. Anal. 7, No. 6, 1096-1142 (1997; Zbl 0902.31004)]. Roughly, this lemma says that two real Brownian motions \(X\) and \(Y\) whose common predictable quadratic variation \(\langle X,Y\rangle\) grows strictly slower than the identity, barely reach together their supremum. Here, corollaries of this result concerning the annulation of some local times are also given as a bonus.
For the entire collection see [Zbl 0893.00035].


60J65 Brownian motion


Zbl 0902.31004
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