Publications

Articles soumis

  • The b-d model of ageing: from individual-based dynamics to evolutive differential inclusions, with M. Rera and T. Roget.
  • Stochastic analysis of emergence of evolutionary cyclic behavior in population dynamics with transfer, with N. Champagnat and C.V. Tran.
  • Horizontal gene transfer: numerical comparison between stochastic and deterministic approaches, with V. Calvez, S. Figueroa Iglesias, H. Hivert, A. Melnykova, S. Nordmann.

Articles publiés

  • Scaling limits of population and evolution processes in random environment, with V. Bansaye and M.E Caballero, To appear in Elect. J. Probab.
  • Diffusions from infinity, with V. Bansaye, P. Collet, S. Martinez, J. San Martin, to appear in TAMS.
  • On time scales and quasi-stationary distributions for multitype birth-and-death processes, with J.R. Chazottes and P. Collet, to appear in Ann. of IHP.
  • Impact of demography on extinction/fixation events, with C. Coron and D. Villemonais, J. Maths Biol. Online, (2018).
  • Feedback between environment and traits under selection in a seasonal environment : consequences for experimental evolution, D. Collot, T. Nidelet, J. Ramsayer, O. Martin, S. Méléard, C. Dillmann, D. Sicard, J. Legrand, Proceedings of the Royal Society B, Vol. 285, No. 1876, (2018).
  • Stochastic dynamics for adaptation and evolution of microorganisms, with S. Billiard, P. Collet, R. Ferrière, V.C. Tran, European Congress of Mathematics Berlin 2016, V. Mehrmann and M. Skutella eds, pp. 525–550, EMS Publishing House, (2018).
  • The effect of competition and horizontal trait hesitance on invasion, fixation and polymorphism, with S. Billiard, P. Collet, R. Ferrière, V.C. Tran, J. Theoret. Biol. 411 (2016), 48–58.
  • Speed of coming down from infinity for birth and death processes, with V. Bansaye and M. Richard, Advances in Applied Probability 48, Issue 4 (2016), 1183–1210.
  • Stochastic eco-evolutionary model of a prey-predator community, with Manon Costa , Céline Hauzy, Nicolas Loeuille. J. Math. Biol. J. Math. Biol. 72 (2016), no. 3, 573-622.
  • Sharp asymptotics for the quasi-stationary distribution of birth-and-death processes, with Jean-René Chazottes and Pierre Collet. Probab. Theory Related Fields. 164 (2016), no. 1-2, 285-332.
  • Stochastic models for structured populations. Scaling limits and long time behavior, with Vincent Bansaye. Mathematical Biosciences Institute Lecture Series. Stochastics in Biological Systems, 1.4. Springer, Cham ; MBI Mathematical Biosciences Institute, Ohio State University, Co- lumbus, OH, 2015.
  • Stochastic dynamics of adaptive trait and neutral marker driven by eco- evolutionary feedbacks, with Sylvain Billiard, Régis Ferrière and Chi Viet Tran. J. Math. Biol. 71 (2015), no. 5, 1211–1242.
  • Influence of a spatial structure on the long time behavior of a competitive Lotka-Volterra type system, with Hélène Leman and Sepideh Mirrahimi. Disc. Cont. Dyn. Syst. - B 20 (2) (2015), 469-493.
  • Singular limits for reaction-diffusion equations with fractional Laplacian and local or nonlocal nonlinearity, with Sepideh Mirrahimi. Comm. Partial Differential Equations 40 (2015), no. 5, 957–993.
  • Non local Lotka-Volterra system with cross-diffusion in an heterogeneous medium, with Joaquin Fontbona. J. Math. Biol. 70 (2015), no. 4, 829–854.
  • Adaptation in a stochastic multi-resources chemostat model, with Nicolas Champagnat and Pierre-Emmanuel Jabin. J. Math. Pures Appl. (9) 101 (2014), no. 6, 755–788.
  • Evolutive two-level population process and large population approximations, with S. Roelly, Annals of the University of Bucharest (mathematical series) 4 (LXII) (2013), 37–70.
  • Quantifying the mutational meltdown in diploid populations, with Camille Coron, Emmanuelle Porcher, Alexandre Robert, The American Naturalist, Vol. 181, No. 5 (Mai 2013), pp. 623–636.
  • Stochastic models for a chemostat and long time behavior, with P. Collet, S. Martinez, J. San Martin, Adv. in Appl. Probab. 45 (3), (2013), 822-836.
  • A rigorous model study of the adaptative dynamics of Mendelian diploids, with P. Collet and J.A.J. Metz, J. Math. Biol., Volume 67, Issue 3 (2013), Page 569–607.
  • Nonlinear historical superprocess approximations for population models with past dependence, with C.V. Tran. Electron. J. Probab., 17 (2012), 1–32. Quasi-stationary distributions and population processes, with D. Villemonais. Probability Surveys, Vol. 9 (2012) 340–410.
  • Slow and fast scales for superprocess limits of age-structure populations, with C.V. Tran, Stoch Process. and Appl., 122 : 250–276 .
  • Lévy flights in evolutionary ecology, with B. Jourdain and W. Woyczynski, J. Math. Biol. 65 (2012), no. 4, 677–707.
  • Quasi-stationarity distributions for structured birth and death process with mutations, with P. Collet, S. Martinez, J. San Martin, Probab. Theory Related Fields, Volume 151, Issue 1 (2011), Page 191–231.
  • Polymorphic evolution sequence and evolutionary branching, with N. Champagnat, Probab. Theory Related Fields, Volume 151, Issue 1 (2011), 45–94.
  • Random Modeling of Adaptive Dynamics and Evolutionary Branching, The mathematics of Darwin’s legacy, F. Chalub J.F. Rodrigues eds, Birhau- ser (2011).
  • Uniform estimates for metastable transition times in a coupled bistable system, with F. Barret et A. Bovier, Electron. J. Probab. 15 (2010), 323– 345.
  • Measurability of optimal transportation and strong coupling of martingale measures, with J. Fontbona et H. Guérin, Electron. C. Probab. 15 (2010), 124–133.
  • Competitive or weak cooperative stochastic Lotka-Volterra systems conditioned on non-extinction, with P. Cattiaux, J. Math. Biology 6 (2010), 797–829.
  • Quasi-stationarity distributions and diffusion models in population dynamics, with P. Cattiaux, P. Collet, A. Lambert, S. Martinez, J. San Martin, Ann. Probab. 37 (2009), no. 5, 1926–1969.
  • Trait substitution sequence process and canonical equation for age-structured populations, with C. Viet Tran, . J. Math. Biol. 58 (2009), no. 6, 881– 921.
  • Measurability of optimal transportation and convergence rate for Landau type interacting particle systems, with J. Fontbona and H. Guérin, Probab. Theory Related Fields 143 (2009), no. 3-4, 329–351.
  • From individual stochastic processes to macroscopic models in adaptive evolution, avec N. Champagnat et R. Ferrière, Stochastic Models (2008), 24 No 1, 2–44.
  • Nonlinear SDEs driven by Lévy processes and related PDEs, with B. Jourdain and W. Woyczynski, Alea 4 (2008), 1–29.
  • A random space-time birth particle method for 2d vortex equations with L1- external field, with J. Fontbona , Math. Comp. 77 (2008), no. 263, 1525–1558.
  • Individual-based probabilistic models of adaptive evolution and various scaling approximations, with N. Champagnat and R. Ferrière, Progress in Probability, Vol. 59 (2007), 75–113, Birhaäuser Verlag Basel.
  • Invasion and adaptive evolution for individual-based spatially structured populations, with N. Champagnat, J. Math. Biology 55 (2007) 147–188.
  • Estimates for the density of a nonlinear Landau process, with H. Guérin and E. Nualart, J. Funct. Anal. 238 (2006) 649–677.
  • Unifying evolutionary dynamics : from individual stochastic processes to macroscopic models, with N. Champagnat and R. Ferrière, Theoretical Population Biology 69 (2006) 297–321.
  • Probabilistic approximation and inviscid limits for 1-D fractional conservation laws, with B. Jourdain and W. Woyczynski, Bernoulli 11 no 4 (2005), 689-714.
  • A probabilistic approach for nonlinear equations involving the fractional Laplacian and a singular operator, with B. Jourdain abd W. Woyczynski, Potential Analysis 23, no 1 (2005), 55-81.
  • The approximate Euler method for Lévy driven stochastic differential equations, with J. Jacod, T. Kurz and P. Protter, Annales de l’IHP, Pro- babilités et statistiques 41, 523-558, (2005).
  • Stochastic particle approximations for two-dimensional Navier-Stokes equations, Dynamics and Randomness II, A. Maass, S. Martinez and J. San Martin eds., Nonlinear Phenomena and Complex Systems, pp. 147-198, Kluwer Academic Publishers (2004).
  • Microscopic probabilistic description of a locally regulated population and macroscopic approximations, with N. Fournier, The Annals of Applied Probability 14, no 4 (2004), 1880-1919.
  • Probabilistic Interpretation and Particle Method for Vortex equations with Neumann’s boundary condition, with B. Jourdain, Proceedings of the Edinburgh Mathematical Society 47 (2004), 597-624.
  • Convergence from Boltzmann to Landau with soft potential and particle approximations, with H. Guérin, J. Statist. Phys. 111, no. 3/4 (2003), 931-966.
  • A weak criterion of absolute continuity for jump processes : application to the Boltzmann equations, with N. Fournier, Bernoulli 8, no. 4 (2002), 537-558.
  • A stochastic particle numerical method for 3D Boltzmann equations without cutoff, with N. Fournier, Math. Comp. 71, no. 238 (2002), 583-604.
  • Probabilistic tools and Monte-Carlo approximations for some Boltzmann equations, with C. Graham, CEMRACS Lecture Notes, July 1999, ESAIM-Proceedings Vol. 10 - CEMRACS, 77-126 (2001).
  • Monte-Carlo approximations of the solution of 2d Navier-stokes equations with finite measure initial data, Probab. Theory .Rel. Fields. 121 (2001), no 3, 367-388.
  • Monte-Carlo approximations for 2D homogeneous Boltzmann equations without cutoff for non Maxwell molecules, with N. Fournier. Monte-Carlo and probabilistic methods for partial differential equations (Monte- Carlo 2000), Monte-Carlo Methods Appl. 7, no. 1-2 (2001), 177-192.
  • A Markov process associated with a Boltzmann equation without cutoff for non Maxwell molecules, with N. Fournier, J. Statist. Phys. 104, no. 1-2 (2001), 359-385.
  • Monte-Carlo approximations and fluctuations for 2D Boltzmann equations without cutoff, with N. Fournier, Inhomogeneous random systems (Cergy- Pontoise 2000), Markov Process. Related Fields 7 (2001), 159-191.
  • A trajectorial proof of the vortex method for the 2d Navier Stokes equation, Ann. Appl. Probab. 10, no. 4, 1197-1211, (2000).
  • The integrand term in the martingale representation theorem, stability results and a Clarke Ocone formula for Markov processes, with Jean Jacod and Philip Protter, Ann. Probab. 28, no. 4, 1747-1780, (2000).
  • Asymptotic behaviour for interacting diffusion processes with space-time random birth, with B. Fernandez, Bernoulli 6, no. 2 (2000), 1-21.
  • Existence and regularity of a solution of a Kac equation without cutoff using Malliavin calculus, with C. Graham, Comm. Math. Phys. 205, no. 3 (1999), 551-570.
  • Probabilistic interpretation and numerical approximation of a Kac equation without cut-off, with C. Graham and L. Desvillettes, Stochastic Pro- cess. Appl. 84, no. 1 (1999), 15-135.
  • Propagation of chaos and fluctuations for a moderate model with smooth initial data, with B. Joudain, Ann. Inst. Henri Poincaré Probab. 34, no. 6 (1998), 727-766.
  • Probabilistic interpretation and approximations of some Boltzmann equations, Lecture Notes of a course in the 5th Symposium in Probability and Stochastic Processes, Aportaciones Matematicas, Modelos Estocaticos 14, Sociedad Matematica Mexicana (1998), 1-64.
  • A large deviations principle for a large star-shaped loss network with links of capacity one, with C. Graham, Markov Process. Related Fields 3, no. 4 (1998), 475-492.
  • Convergence of the fluctuations for interacting diffusions with jumps associated with Boltzmann equations, Stochastics Stochastic Rep. 63, no. 3+4 (1998), 195-225.
  • Stochastic approximations of the solution of a full Boltzmann equation for small initial data, ESAIM http ://www.emath.fr/ps/., Vol. 2 (1998), 23-40.
  • An upperbound of large deviations for a generalized star-shaped loss network, with C. Graham, Markov Process. Related Fields 3, no. 2 (1997), 199-223.
  • A Hilbertian approach for fluctuations on the McKean-Vlasov model, with B. Fernandez, Stochastic Process. Appl. 71 (1997), 33-53.
  • Stochastic particle approximations for generalized Boltzmann models and convergence estimates, with C. Graham, Ann. Probab. 25, no. 1 (1997), 115-132.
  • Convergence rate on path space for stochastic particle approximations to the Boltzmann equation, with C. Graham, Proceedings ICIAM 95, Numerical Analysis, Ed. G. Alefeld, Special issue ZAMM (1996).
  • Asymptotic behaviour of some interacting particle systems McKean-Vlasov and Boltzmann models, C.I.M.E. Lecture Notes, Probabilistic models for nonlinear partial differential equations May 1995, L.N. in Math. 1627 (1996), 42-95, Springer.
  • Dynamic asymptotic results for a generalized star-shaped loss network, with C. Graham, Ann. Appl. Probab. 5, no. 3 (1995), 666-680.
  • Chaos hypothesis for a system interacting through shared ressources, with C. Graham, Probab. Theory Related Fields 100 (1994), 157-173.
  • Fluctuations for a completely connected loss network, with C. Graham, Stochastic Process. Appl. 53 (1994), 97-11.
  • Sur les convergences étroite ou vague de processus à valeurs mesures, with S. Roelly, CRAS de l’Acad. des Sci. Paris, t. 317, Série I ( 1993), 785-788.
  • Interacting measure branching processes. Some bounds for the support, withS. Roelly, Stochastics Stochastic Rep. 44, no. 1+2 (1993), 103-121.
  • Propagation of chaos for a fully connected loss network with alternate routing, with C. Graham, Stochastic Process. Appl. 44, no. 1 (1993), 159-180.
  • Representation and approximation of martingale measures, Proceedings IFIP W 7/1 International Conference University North carolina at Charlotte (1992), 188-199, L.N. in Control and Information Sciences, Springer.
  • An ergodic result for critical spatial branching processes, with S. Roelly, Proceedings Stochastic analysis and Related topics (1992), 333-342, Birkhäuser.
  • Interacting measure branching processes, with S. Roelly, Proceedings Stochastic partial differential equations, Pitman research notes in Mathematics 268 (1992), 246-256, Longman Scientific and technical.
  • Discontinuous measure-valued branching processes and generalized stochastic equations, with S. Roelly, Math. Nachr. 154 (1991), 141-156.
  • Martingale measures and stochastic calculus, with N. El Karoui, Probab.Theory Rel. Fields 84 (1990), 83-101.
  • Some stochastic models of interacting diffusion processes and the associated propagation of chaos, Proceedings, Stochastic Modelling in Biology, Heidelberg (1990), 107-125, World Scientific.
  • A generalized equation for a continuous measure branching process, with S. Roelly, Proceedings Trento 1988 (Stochastic Partial Differential Equations and Applications II), L.N. 1390 (1989), 171-185, Springer.
  • Systèmes de particules et mesures martingales : un théorème de propaga- tion du chaos, with S. Roelly, Séminaire de Probabilités 22, L.N. 1321, Springer, (1988), 438-448.
  • A propagation of chaos result for a system of particles with moderate interaction, with S. Roelly, Stochastic Process. Appl. 26, no. 2, (1987), 317-332.
  • Application du calcul stochastique à l’étude des processus de Markov réguliers sur [0, 1], Stochastics Stochastics Rep. 19, no. 1+2, (1986), 41-8


Publications pédagogiques


  • Modèles aléatoires en écologie et évolution, Mathématiques et Applications 77, SMAI. Springer, 2016.
  • Stochastic Models for Structured Populations, with V. Bansaye, MBI Lecture Series 1.4, Springer, 2015.
  • Processus de branchement. Applications en écologie, Aléatoire, 1–51, Editions de l’Ecole Polytechnique, 2013.
  • Aléatoire : Introduction à la théorie et au calcul des probabilités, Editions de l’Ecole Polytechnique, Ellipses, (2010).
  • Nos 20 sujets préférés, CAPES de Mathématiques, with F. Bories-Longuet, A. Descomps-Guilloux, P. Jarraud, C. Piquet, Dunod, (2000).
  • Les Bases de l’Analyse, tomes 1 et 2, with J.Y. Chevalier, B. Ozerée et O. Salon, Dunod (1990,1991).
  • Ecrit du CAPES, Analyse et Probabilités, with C. Piquet, Masson (1992).



  • "Encyclopédie des Techniques de l’Ingénieur" :
  • Présentation des probabilités, AF164 “Techniques de l’ingénieur”, (2001). Résumé de la théorie de la mesure et intégration, AF165 “Techniques de l’ingénieur”, (2002).
  • Probabilités, Concepts fondamentaux, AF166 “Techniques de l’ingénieur”, (2002).
  • Mouvement brownien et calcul stochastique, “Techniques de l’ingénieur”, (2003).


  • Approche probabiliste pour l’étude d’équations aux dérivées partielles non linéaires issues de la mécanique des fluides, MATAPLI (2001).
  • Les différentes échelles de temps de l’évolution, with Vincent Bansaye and Amandine Veber, MATAPLI 100 (2013).
  • Modélisation aléatoire de la biodiversité: de l'importance des paramètres d'échelle. (French) [Stochastic models of biodiversity: on the importance of scale parameters] Gaz. Math. No. 154 (2017), 7–20.