Density of paths of iterated Lévy transforms of Brownian motion

Malric, Marc. "Density of paths of iterated Lévy transforms of Brownian motion." ESAIM: Probability and Statistics 16 (2012): 399-424. <http://eudml.org/doc/222464>.

@article{Malric2012,
abstract = {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 (t → Bt(n))n⩾0 is dense in Wiener space, for the topology of uniform convergence on compact time intervals.},
author = {Malric, Marc},
journal = {ESAIM: Probability and Statistics},
keywords = {Brownian motion; Lévy transform; excursions; zeroes of Brownian motion; ergodicity; topological recurrence},
language = {eng},
month = {8},
pages = {399-424},
publisher = {EDP Sciences},
title = {Density of paths of iterated Lévy transforms of Brownian motion},
url = {http://eudml.org/doc/222464},
volume = {16},
year = {2012},
}

TY - JOUR
AU - Malric, Marc
TI - Density of paths of iterated Lévy transforms of Brownian motion
JO - ESAIM: Probability and Statistics
DA - 2012/8//
PB - EDP Sciences
VL - 16
SP - 399
EP - 424
AB - 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 (t → Bt(n))n⩾0 is dense in Wiener space, for the topology of uniform convergence on compact time intervals.
LA - eng
KW - Brownian motion; Lévy transform; excursions; zeroes of Brownian motion; ergodicity; topological recurrence
UR - http://eudml.org/doc/222464
ER -