My main research interests are:

  • Conditionings and path decompositions of Markov processes.
  • Perturbed Brownian motion.
  • Fluctuation theory for random walks and Lévy processes.
  • Selfsimilar Markov processes.
  • Branching processes and random trees.
  • Stochastic models of population dynamics



  • Research papers


  • Coding multitype branching forests: application to the law of the total progeny.
        (With R. Liu) Preprint LAREMA, (2013).

  • Timing of pathogen adaptation to a multicomponent treatment.
        (With R. Bourget and N. Sapoukhina) Preprint LAREMA, (2012).

  • An invariance principle for random walk bridges conditioned to stay positive.
        (With F. Caravenna) Preprint LAREMA, (2012).

  • Exponentiality of first passage times of continuous time Markov chains.
        (With R. Bourget and N. Sapoukhina) Preprint LAREMA, (2012).

  • The Lamperti representation of real-valued self-similar Markov processes.
        (With H. Pantí and V. Rivero) To appear in Bernoulli, (2012).

  • On the law of the supremum of Lévy processes.
        
    Ann. Probab., Vol. 41, No. 3A, 1191-1217, (2013).

  • Fluctuation theory and exit systems for positive self-similar Markov processes.
        
    (With A.E Kyprianou, J.C. Pardo and V. Rivero) Ann. Probab., Vol. 40, No. 1, 245-279, (2012).

  • Markovian Bridges: Weak continuity and pathwise constructions.
         (With G. Uribe Bravo) Ann. Probab., Vol. 39, No. 2, 609-647, (2011).

  • Invariance principles for local times at the supremum of random walks and Lévy processes.
         (With R.A. Doney) Ann. Probab., Vol. 38, No. 4, 1368-1389, (2010).

  • Reflection principle and Ocone martingales. (With L. Vostrikova)
         Stochastic Process. Appl., Vol. 119, No. 10, 3816-3833, (2009).

  • On the genealogy of conditioned stable Lévy forests. (With J.C. Pardo)
         Alea 6, 261-279, (2009).

  • Some explicit identities associated with positive self-similar Markov processes.
         (With A.E Kyprianou and J.C. Pardo) Stochastic Process. Appl., Vol. 119, No. 3, 980-1000, (2009).

  • Invariance principles for random walks conditioned to stay positive. (With F. Caravenna)
         Annales de l'Institut Henri Poincaré, Vol. 44, No. 1, 170-190, (2008).

  • On some transformations between positive self-similar Markov processes. (With V. Rivero)
        Stochastic Process. Appl., 117, No. 12, 1889--1909, (2007).

  • Conditioned stable Lévy processes and Lamperti representation. (With M.E. Caballero)
        J. Appl. Prob. 43, 967--983, (2006).

  • The lower envelope of positive self-similar Markov processes. (With J.C Pardo)
        Electron. J. Probab. Vol. 11, (2006), No. 49, 1321--1341.

  • Weak convergence of positive self similar Markov processes and
        overshoots of Lévy processes.
    (With M.E. Caballero)
        Ann. Probab. Vol. 34, No. 3, 1012-1034, (2006).

  • On Lévy processes conditionned to stay positive. (With R.A. Doney)
        Electron. J. Probab. 10, (2005), no. 28, 948--961.

  • On a fluctuation identity for random walks and Lévy processes. (With L. Alili and R.A. Doney)
        Bull. London Math. Soc. 37, (2005), 141-148.

  • Path transformations of first passage bridges. (With J. Bertoin and J. Pitman)
        Elect. Comm. in Probab., 8 (2003), 155--166.

  • A new fluctuation identity for Lévy processes and some applications. (With L. Alili)
        Bernoulli 7 (3), 2001, 557-569.

  • Some consequences of the cyclic exchangeability property
        for exponential functionals of Lévy processes.
    (With D.G. Hobson and M. Yor)
        Séminaire de Probabilités, XXXV, 334-347, Lecture Notes in Math., 1755, Springer, Berlin, 2001.

  • An extension of Vervaat's transformation and its consequences.
         J. Theoret. Probab. 13 (2000), no. 1, 259--277.

  • Upper and lower limits of doubly perturbed Brownian motion. (With R.A. Doney and Y. Hu)
        Ann. Inst. H. Poincaré Probab. Statist. 36 (2000), no. 2, 219--249.

  • Some calculations for doubly perturbed Brownian motion. (With R.A. Doney)
        Stochastic Process. Appl. 85 (2000), no. 1, 61--74.

  • Pathwise uniqueness for perturbed versions of Brownian motion and reflected
        Brownian motion. (With R.A. Doney)
        Probab. Theory Related Fields 113 (1999), no. 4, 519--534.

  • A path transformation and its applications to fluctuation theory.
        J. London Math. Soc. (2) 59 (1999), no. 2, 729--741.

  • Two chain-transformations and their applications to quantiles. (With J. Bertoin and M. Yor)
        J. Appl. Probab. 34 (1997), no. 4, 882--897.

  • Excursion normalisée, méandre et pont pour les processus de Lévy stables.
        Bull. Sci. Math. 121 (1997), no. 5, 377--403.

  • Conditionings and path decompositions for Lévy processes.
        Stochastic Process. Appl. 64 (1996), no. 1, 39--54.

  • Sur certains processus de Lévy conditionnés à rester positifs.
        Stochastics and Stoch. Rep. (1994) Vol. 47, pp. 1--20.



  • Books


  • Introduction aux processus auto-similaires.
        Preliminary version, (2010).

  • Exercises in Probability
        A Guided Tour from Measure Theory to Random Processes, via Conditioning.

        Cambridge University Press. (With M. Yor)
        First edition 2003 Second edition 2012



  • Proceedings, history of mathematics, popularization,...


  • Self-similar processes and their applications.
         Séminaires et Congrès, SMF, Vol. 28, 2012. L. Chaumont, L. Vostrikova and P. Graczyk (Eds.)

  • X Symposium on Probability and Stochastic Processes and the First Joint Meeting France-Mexico of Probability.
         Proceedings of the sympsoium and the meeting held in Guanajuato, November 3--7, 2008.

         ESAIM: Proceedings, Vol. 31 (January 2011). M.E. Caballero, L. Chaumont, D. Hernández-Hernández and V. Rivero (Eds.)

  • Des aléas à prévoir Revue Têtes Chercheuses, (2010).
        Journal scientifique trimestriel destiné aux lycéens.

  • Corrections to "On Lévy processes conditioned to stay positive" (With R.A. Doney)
        Electron. J. Probab. Vol. 13, (2008), No. 1, 1-4.

  • Some aspects of the probabilistic work. (With Laurent Mazliak et Marc Yor)
        Kolmogorov's heritage in mathematics, 41-66, Springer, Berlin, (2007), No. 1, 1-4.

  • Kolmogorov : Quelques aspects de l'oeuvre probabiliste. (With Laurent Mazliak et Marc Yor)
        (chapitre de livre extrait de L'héritage de Kolmogorov en mathématiques, Editions Belin, 2004)

  • Quelques nouvelles identités de fluctuation pour les processus de Lévy. (With L. Alili)
        C. R. Acad. Sci. Paris Sér. I Math. 328 (1999), no. 7, 613-616.

  • Path transformations in Lévy processes.
        Bull. of the Int. Stat. Inst., Tome LVIII, Helsinki, (1999), Book 1, 459-462.

  • Excursion normalisée, pont et méandre pour les processus stables.
        C. R. Acad. Sci. Paris Sér. I Math. 318 (1994), no. 6, 563-566.