# Reflection principle and Ocone martingales

@article{Chaumont2008ReflectionPA,
title={Reflection principle and Ocone martingales},
author={Lo{\"i}c Chaumont and L. P. Vostrikova},
journal={Stochastic Processes and their Applications},
year={2008},
volume={119},
pages={3816-3833}
}
• Published 24 July 2008
• Mathematics
• Stochastic Processes and their Applications
3 Citations
Characterising Ocone Local Martingales with Reflections
• Mathematics
• 2013
Let M = (M t ) t ≥ 0 be any continuous real-valued stochastic process such that M 0 = 0. Chaumont and Vostrikova proved that if there exists a sequence (a n ) n ≥ 1 of positive real numbers
Pricing and hedging exotic options in stochastic volatility models
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## References

SHOWING 1-10 OF 17 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,
Transformation de Lévy et zéros du mouvement Brownien
AbstractIn this paper, it is shown that the iterated Lévy transforms (βn) of a standard Brownian motion β, so defined: \beta ^0 = \beta ,and:\beta _t^{n + 1} = \int\limits_0^t {\operatorname{sgn}
Limit Theorems for Stochastic Processes
• Mathematics
• 1987
I. The General Theory of Stochastic Processes, Semimartingales and Stochastic Integrals.- II. Characteristics of Semimartingales and Processes with Independent Increments.- III. Martingale Problems
Density of paths of iterated Lévy transforms of Brownian motion
The Levy transform of a Brownian motion B is the Brownian motion B (1) given by B t (1) = ∫ 0 t sgn(Bs )dBs ; call B (n ) the Brownian motion obtained from B by iterating n times this transformation.
On the Lévy transformation of brownian motions and continuous martingales
• Mathematics
• 1993
© 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
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
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
Yor: Some invariance properties (of the laws) of Ocone’s martingales. Séminaire de Probabilités, XXXIV, 417–431
• Lecture Notes in Math.,
• 2000
Solution directe du problème résolu par M . Bertrand
• Séminaire de Probabilités
• 1993