# Density of paths of iterated Lévy transforms of Brownian motion

ESAIM: Probability and Statistics (2012)

- Volume: 16, page 399-424
- ISSN: 1292-8100

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topMalric, 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 -

## References

top- L.E. Dubins and M. Smorodinsky, The modified, discrete Lévy transformation is Bernoulli, in Séminaire de Probabilités XXVI. Lect. Notes Math.1526 (1992)
- M. Malric, Densité des zéros des transformées de Lévy itérées d’un mouvement brownien. C. R. Acad. Sci. Paris, Sér. I336 (2003) 499–504.
- D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, 3th edition. Springer-Verlag, Berlin (1999)

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