Densité des zéros des transformés de Lévy itérés d’un mouvement brownien. (Density of zeros for iterated Lévy transforms of Brownian motion). (French. Abridged English version) Zbl 1024.60034

Summary: The Lévy transform of a Brownian motion \(B\) is the Brownian motion
\(B_t'=\int^t_0 \text{sgn} B_sdB_s\); denote by \(B^n\) the Brownian motion obtained from \(B\) by iterating \(n\) times the Lévy transform. We establish that the set of all instants \(t\) such that \(B^n_t=0\) for some \(n\), is a.s. dense in the time-axis \(\mathbb{R}_+\).


60J65 Brownian motion
60H05 Stochastic integrals
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