# On the Lévy transformation of brownian motions and continuous martingales

@inproceedings{Dubins1993OnTL,
title={On the L{\'e}vy transformation of brownian motions and continuous martingales},
author={Lester E. Dubins and Michel {\'E}mery and Marc Yor},
year={1993}
}
• Published 1993
• Mathematics
© Springer-Verlag, Berlin Heidelberg New York, 1993, tous droits réservés. L’accès aux archives du séminaire de probabilités (Strasbourg) (http://portail. mathdoc.fr/SemProba/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
Some invariance properties (of the laws) of Ocone's martingales
• Mathematics
• 2000
© Springer-Verlag, Berlin Heidelberg New York, 2000, tous droits réservés. L’accès aux archives du séminaire de probabilités (Strasbourg) (http://portail. mathdoc.fr/SemProba/) implique l’accord avec
Some Sufficient Conditions for the Ergodicity of the Lévy Transformation
We propose a possible way of attacking the question posed originally by Daniel Revuz and Marc Yor in their book published in 1991. They asked whether the Levy transformation of the Wiener-space is
Some sufficient conditions for the ergodicity of the L\'evy transformation
We propose a possible way of attacking the question posed originally by Daniel Revuz and Marc Yor in their book published in 1991. They asked whether the Lévy transformation of the Wiener–space is
Strong approximation of continuous local martingales by simple random walks
• Mathematics
• 2004
The aim of this paper is to represent any continuous local martingale as an almost sure limit of a nested sequence of simple, symmetric random walk, time changed by a discrete quadratic variation
The joint law of the last zeros of Brownian motion and of its Lévy transform
• Mathematics
Ergodic Theory and Dynamical Systems
• 2000
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
Credit Dynamics in a First Passage Time Model with Jumps
• Mathematics, Economics
• 2010
The payoff of many credit derivatives depends on the level of credit spreads. In particular, the payoff of credit derivatives with a leverage component is sensitive to jumps in the underlying credit
Continuous Ocone martingales as weak limits of rescaled martingales
Consider a martingale $M$ with bounded jumps and two sequences $a_n, b_n \to \infty$. We show that if the rescaled martingales $$M^n_t =\frac{1}{\sqrt{a_n}}M_{b_n t}$$ converge weakly, then the
A random walk analogue of Lévy’s Theorem
In this paper we will give a simple symmetric random walk analogue of Levy’s Theorem. We will give a new definition of a local time of the simple symmetric random walk. We apply a discrete Ito
Ja n 20 12 Self-dual continuous processes
• Mathematics
• 2012
The important application of semi-static hedging in financial markets naturally leads to the notion of quasi self-dual processes which is, for continuous semimartingales, related to symmetry

## References

SHOWING 1-7 OF 7 REFERENCES
The modified, discrete Lévy transformation is Bernoulli
• Mathematics
• 1992
From the absolute value of a martingale, X, there is a unique increasing process that can be subtracted so as to obtain a martingale, Y. Paul Levy discovered that if X is Brownian motion, B, then Y,
Continuous martingales and Brownian motion
• Mathematics
• 1990
0. Preliminaries.- I. Introduction.- II. Martingales.- III. Markov Processes.- IV. Stochastic Integration.- V. Representation of Martingales.- VI. Local Times.- VII. Generators and Time Reversal.-
A Symmetry Characterization of Conditionally Independent Increment Martingales
We show that a cadlag, local martingale has conditionally independent increments and symmetric jumps if and only if its law is invariant under integral transformations which preserve quadratic
ON CONTINUOUS MARTINGALES.
• Mathematics
Proceedings of the National Academy of Sciences of the United States of America
• 1965