Density of zeros for iterated Levy transforms of Brownian motion

The Levy transform of a Brownian motion B is the Brownian motion B'(t) = integral(0)(t) sgn B-s dB(s); denote by B-n the Brownian motion obtained from B by iterating n times the Uvy transform. We establish that the set of all instants t such that B-t(n) = 0 for some n, is a.s. dense in the time-axis R+. (C) 2003 Published by Academie des sciences/Editions scientifiques et medicales Elsevier SAS.