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
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