Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-26T00:48:45.849Z Has data issue: false hasContentIssue false
  • English
  • Français

The joint law of the last zeros of Brownian motion and of its Lévy transform

Published online by Cambridge University Press:  01 June 2000

CATHERINE DONATI-MARTIN ,
ZHAN SHI  and
MARC YOR
CATHERINE DONATI-MARTIN
Affiliation:
Laboratoire de Statistique et Probabilités, Université Paul Sabatier Toulouse III, 118 route de Narbonne, F-31062 Toulouse Cedex 04, France
ZHAN SHI
Affiliation:
Laboratoire de Probabilités, Université Paris VI, 4 Place Jussieu, F-75252 Paris Cedex 05, France
MARC YOR
Affiliation:
Laboratoire de Probabilités, Université Paris VI, 4 Place Jussieu, F-75252 Paris Cedex 05, France
Get access Rights & Permissions [Opens in a new window]

Abstract

The joint study of functionals of a Brownian motion $B$ and its Lévy transform $\beta= |B|-L$, where $L$ is the local time of $B$ at zero, is motivated by the conjectured ergodicity of the Lévy transform.

Here, we compute explicitly the covariance of the last zeros before time one of $B$ and $\beta$, which turns out to be strictly positive.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 20 , Issue 3 , June 2000 , pp. 709 - 725
Copyright
2000 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)