×

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 \(\mathbb{R}_+\).

MSC:

60J65 Brownian motion
60H05 Stochastic integrals
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Malric, M., Transformation de Lévy et zéros du mouvement brownien, Probab. theory related fields, 101, 227-236, (1995) · Zbl 0820.60062
[2] Revuz, D.; Yor, M., Continuous martingales and Brownian motion, (1999), Springer-Verlag Berlin · Zbl 0917.60006
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.