Research

Homepage of Loïc Chaumont




My main research interests are:

  • Fluctuation theory for random walks and Lévy processes.
  • Selfsimilar Markov processes.
  • Branching processes and random trees.
  • Stochastic models of population dynamics



  • Research papers


  • Space and time inversions of stochastic processes and Kelvin transform
        (With Larbi Alili, Piotr Graczyk and Tomasz Żak) Preprint Arxiv, (2017).

  • On distributions determined by their upward, space-time Wiener-Hopf factor.
        (With Ron Doney) Preprint Arxiv, (2017).

  • On mutations in the branching model for multitype populations.
        (With Thi Ngoc Anh Nguyen) Preprint Arxiv, (2016).

  • Inversion, duality and Doob h-transforms for self-similar Markov processes
        (With Larbi Alili, Piotr Graczyk and Tomasz Żak) Electron. J. Probab. 22, no. 20, 1-18, (2017).

  • Reconstructing pedigrees using probabilistic analysis of ISSR amplification.
        (With Valéry Malécot, Richard Pymar and Chaker Sbai) Journal of Theoretical Biology 412, 8-16, (2017).

  • The asymptotic behavior of the density of the supremum of Lévy processes.
        (With J. Małecki) Annales de l'Institut Henri Poincaré, Vol. 52, No. 3, 1178-1195, (2016).

  • Coding multitype forests: application to the law of the total population of branching forests.
        (With R. Liu) Trans. Amer. Math. Soc. 368, no. 4, 2723-2747, (2016).

  • Breadth first search coding of multitype forests with application to Lamperti representation.
         Lecture Notes in Mathematics, Volume 2137, In Memoriam Marc Yor
         Séminaire de Probabilités XLVII, 561-584, (2015).

  • Shifting processes with cyclically exchangeable increments at random.
        (With G. Uribe Bravo) XI Symposium on Probability and Stochastic Processes,
         Birkhäuser series Progress in Probability, Volume 69 of the series Progress in Probability, 101-117, (2015).

  • Sustainable deployment of QTLs conferring quantitative resistance to crops: first lessons from a stochastic model.
        (With R. Bourget, C.E. Durel and N. Sapoukhina) New Phytologist, doi: 10.1111/nph.13295, (2015).

  • Exponentiality of first passage times of continuous time Markov chains.
        (With R. Bourget and N. Sapoukhina) Acta Appl. Math. 131, 197-212, (2014).

  • The Lamperti representation of real-valued self-similar Markov processes.
        (With H. Pantí and V. Rivero) Bernoulli 19(5B), 2494-2523, (2013).

  • Timing of Pathogen Adaptation to a Multicomponent Treatment.
        (With R. Bourget and N. Sapoukhina) PLoS ONE 8(8): e71926. doi:10.1371/ journal.pone.0071926, (2013).

  • An invariance principle for random walk bridges conditioned to stay positive.
        (With F. Caravenna) Electron. J. Probab. 18, no. 60, 1-32, (2013).

  • 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.