Density of paths of iterated Lévy transforms of brownian motion
ESAIM: Probability and Statistics, Tome 16 (2012), pp. 399-424.

The Lévy transform of a Brownian motion B is the Brownian motion B(1) given by Bt(1) = 0tsgn(Bs)dBs; call B(n) the Brownian motion obtained from B by iterating n times this transformation. We establish that almost surely, the sequence of paths (tBt(n))n⩾0 is dense in Wiener space, for the topology of uniform convergence on compact time intervals.

DOI : https://doi.org/10.1051/ps/2011020
Classification : 60g99,  60j65,  37a05,  37a50,  37a25
Mots clés : brownian motion, Lévy transform, excursions, zeroes of brownian motion, ergodicity
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author = {Malric, Marc},
title = {Density of paths of iterated {L\'evy} transforms of brownian motion},
journal = {ESAIM: Probability and Statistics},
pages = {399--424},
publisher = {EDP-Sciences},
volume = {16},
year = {2012},
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zbl = {1274.60171},
mrnumber = {2972500},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps/2011020/}
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Malric, Marc. Density of paths of iterated Lévy transforms of brownian motion. ESAIM: Probability and Statistics, Tome 16 (2012), pp. 399-424. doi : 10.1051/ps/2011020. http://archive.numdam.org/articles/10.1051/ps/2011020/

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