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}
}
© 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. 
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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,
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0. Preliminaries.- I. Introduction.- II. Martingales.- III. Markov Processes.- IV. Stochastic Integration.- V. Representation of Martingales.- VI. Local Times.- VII. Generators and Time Reversal.-
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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
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On the Decomposition of Continuous Submartingales