# 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/274368>.

@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},

pages = {399-424},

publisher = {EDP-Sciences},

title = {Density of paths of iterated Lévy transforms of brownian motion},

url = {http://eudml.org/doc/274368},

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

PY - 2012

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/274368

ER -

## References

top- [1] L.E. Dubins and M. Smorodinsky, The modified, discrete Lévy transformation is Bernoulli, in Séminaire de Probabilités XXVI. Lect. Notes Math. 1526 (1992) Zbl0761.60043
- [2] M. Malric, Densité des zéros des transformées de Lévy itérées d’un mouvement brownien. C. R. Acad. Sci. Paris, Sér. I 336 (2003) 499–504. Zbl1024.60034MR1975087
- [3] D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, 3th edition. Springer-Verlag, Berlin (1999) Zbl0731.60002MR1725357