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}
}
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References

SHOWING 1-7 OF 7 REFERENCES
The modified, discrete Lévy transformation is Bernoulli
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
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…
Application de la theorie du grossissement a l'etude des temps locaux Browniens
Grossissements de filtrations: exemples et applications
ON CONTINUOUS MARTINGALES.
  • L. Dubins, G. Schwarz
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1965
On the Decomposition of Continuous Submartingales