Nicolas Fournier

Professeur au LPSM
Couloir 16-26, bureau 219
Tél : 01 44 27 70 42
nicolas.fournier@sorbonne-universite.fr

Processus de sauts (M1) : cours, exercices.
Compléments de probabilités (M2) : cours.
Calcul stochastique (M2) : cours, exercices, examen 2025.

• with S. Mischler. Propagation of chaos for the homogeneous Boltzmann equation with moderately soft potentials
• with L. Béthencourt, appendix by L. Mazet. On reflected isotropic stable processes. 76 pages.
• with S. Delattre. Markov decision processes: on the convergence of the Monte-Carlo first visit algorithm. 25 pages.
• On gelation for the Smoluchowski coagulation equation. C. R. Math. Acad. Sci. Paris 363, 583-591, 2025.
• with Y. Tardy. Collisions of the supercritical Keller-Segel particle system. J. Eur. Math. Soc. Vol. 27, 4082-4158, 2025. Simulations.
• Convergence of the empirical measure in expected Wasserstein distance: non asymptotic explicit bounds in Rd. ESAIM P&S. Vol. 27, 749-775, 2023.
• with M. Tomašević. Particle approximation of the doubly parabolic Keller-Segel equation in the plane. J. Funct. Anal. Vol. 285, article 110064, 35 pages, 2023.
• with Y. Tardy. A simple proof of non-explosion for measure solutions of the Keller-Segel equation. Kinet. Relat. Models. Vol. 16, 178-186, 2023.
• with A. Bernou. A coupling approach for the convergence to equilibrium for a collisionless gas. Ann. Appl. Probab. Vol. 32, 764--811, 2022.
• with B. Perthame. A non-expanding transport distance for some structured equations. SIAM J. Math. Anal. Vol. 53, 6847-6872, 2021.
• On exponential moments of the homogeneous Boltzmann equation for hard potentials without cutoff. Comm. Math. Phys. Vol. 387, 973-994, 2021.
• with D. Heydecker. Stability, well-posedness and regularity of the homogeneous Landau equation for hard potentials. Ann. Inst. H. Poincaré Anal. Non Linéaire. Vol. 38, 1961-1987, 2021.
• with C. Tardif. On the simulated annealing in Rd. J. Funct. Anal., Vol. 281, article 109086, 30 pages, 2021.
• with P. Monmarché, C. Tardif. Simulated annealing in Rd with slowly growing potentials. Stochastic Process. Appl., Vol. 131, 276-291, 2021.
• with C. Tardif. One-dimensional critical kinetic Fokker-Planck equations, Bessel and Stable processes. Comm. Math. Phys., Vol. 381, 143-173, 2021.
• with C. Tardif. Anomalous diffusion for multi-dimensional critical kinetic Fokker-Planck equations. Ann. Probab., Vol. 48, 2359-2403, 2020.
• with B. Perthame. Transport costs for PDEs: the coupling method. EMS Surv. Math. Sci., Vol. 7, 1-31, 2020. Erratum
• with E. Tanré, R. Veltz. On a toy network of neurons interacting through their dendrites. Ann. Inst. H. Poincaré Probab. Statist., Vol. 56, 1041-1071, 2020.
• with S. Delattre, On Monte-Carlo tree search for deterministic games with alternate moves and complete information. ESAIM P&S, Vol. 23, 176-216, 2019. Code
• A recursive algorithm and a series expansion related to the homogeneous Boltzmann equation for hard potentials with angular cutoff. Kinet. Relat. Models. Vol. 12, 483-505, 2019.
• with L. Xu. On the equivalence between some jumping SDEs with rough coefficients and some non-local PDEs. Ann. Inst. H. Poincaré Probab. Statist. Vol. 55, 1163-1178, 2019.
• with S. Delattre, On the Kozachenko-Leonenko entropy estimator. J. Statist. Plann. Inference, Vol. 185, 69-93, 2017.
• with B. Jourdain. Stochastic particle approximation of the Keller-Segel equation and two-dimensional generalization of Bessel processes. Ann. Appl. Probab., Vol 27, 2807-2861, 2017.
• with A. Guillin. From a Kac-like particle system to the Landau equation for hard potentials and Maxwell molecules. Ann. Sci. Éc. Norm. Supér., Vol 50, 157-199, 2017.
• with S. Delattre, Statistical inference versus mean field limit for Hawkes processes. Electron. J. Stat., Vol. 10, 1223-1295, 2016.
• with M. Hauray. Propagation of chaos for the Landau equation with moderately soft potentials. Ann. Probab., Vol. 44, 3581-3660, 2016. Erratum
• with E. Löcherbach. On a toy model of interacting neurons. Ann. Inst. H. Poincaré Probab. Statist., Vol. 52, 1844-1876, 2016.
• with S. Delattre, M. Hoffmann. Hawkes processes on large networks. Ann. Appl. Probab., Vol. 26, 216-261, 2016.
• with S. Mischler. Rate of convergence of the Nanbu particle system for hard potentials and Maxwell molecules. Ann. Probab., Vol. 44, 589-627, 2016.
• with A. Guillin. On the rate of convergence in Wasserstein distance of the empirical measure. Probab. Theory Related Fields, Vol. 162, 707-738, 2015. Erratum
• Finiteness of entropy for the homogeneous Boltzmann equation with measure initial condition. Ann. Appl. Probab., Vol. 25, No 2, 860-897, 2015.
• with X. Bressaud. Mean-field forest-fire models and pruning of random trees. Version sans arbres "A mean-field forest-fire model", ALEA Lat. Am. J. Probab. Math. Stat. Vol. XI, 589-614, 2014.
• with M. Hauray, S. Mischler. Propagation of chaos for the 2D viscous vortex model. J. Eur. Math. Soc., Vol. 16, No 7, 1423-1466, 2014.
• with X. Bressaud. One-dimensional general forest fire processes. Mém. Soc. Math. Fr., Vol. 132, vi+138 pages, 2013.
• with A. Debussche. Existence of densities for stable-like driven SDE's with Hölder continuous coefficients. J. Funct. Anal., Vol. 264, No 8, 1757-1778, 2013.
• On pathwise uniqueness for stochastic differential equations driven by stable Lévy processes. Ann. Inst. H. Poincaré Probab. Statist., Vol. 49, 138-159, 2013.
• with D. Godinho. Asymptotics of grazing collisions and particle approximation for the Kac equation without cutoff. Comm. Math. Phys., Vol. 316, 307-344, 2012.
• with E. Cepeda. Smoluchowski's coagulation equation: rate of convergence of the Marcus-Lushnikov process. Stochastic Process. Appl., Vol. 121, Issue 6, 1411-1444, 2011.
• with J. Printems. Stability of the stochastic heat equation in L1([0,1]). Electron. Comm. Probab., Vol. 16, 337-352, 2011.
• with V. Bally. Regularization properties of the 2D homogeneous Boltzmann equation without cutoff. Probab. Theory Related Fields, Vol. 151, no 3-4, 659-704, 2011.
• Simulation and approximation of Lévy-driven stochastic differential equations. ESAIM P&S, Vol. 15, 249-269, 2011.
• Uniqueness of bounded solutions for the homogeneous Landau equation with a Coulomb potential. Comm. Math. Phys., Vol. 299, no 3, 765-782, 2010.
• with J. Barral, with S. Jaffard, S. Seuret. A pure jump Markov process with a random singularity spectrum. Ann. Probab., Vol. 38, no 5, 1924-1946, 2010.
• with X. Bressaud. Asymptotics of one-dimensional forest fire processes. Ann. Probab., Vol. 38, no 5, 1783-1816, 2010.
• with with J. Printems. Absolute continuity of some one-dimensional processes. Bernoulli, Vol. 16, 2, 343-360, 2010.
• Particle approximation of some Landau equations. Kinet. Relat. Models, Vol. 2, 3, 451 - 464, 2009.
• with C. Mouhot. On the well-posedness of the spatially homogeneous Boltzmann equation with a moderate angular singularity. Comm. Math. Phys., Volume 289, 3, 803-824, 2009. Important Erratum
• with H. Guérin. Well-posedness of the spatially homogeneous Landau equation for soft potentials. J. Funct. Anal., Volume 256, 9, 2542-2560, 2009.
• with X. Bressaud. On the invariant distribution of an avalanche process. Ann. Probab., Volume 37, No 1, Pages 48-77, 2009.
• with P. Laurencot. Marcus Lushnikov processes, Smoluchowski's and Flory's models. Stochastic Process. Appl., Volume 119, Issue 1, Pages 167-189, 2009.
• with E. Löcherbach. Stochastic coalescence with homogeneous-like interaction rates. Stochastic Process. Appl., Volume 119, Issue 1, Pages 45-73, 2009.
• A new regularization possibility for the Boltzmann equation with soft potentials. Kinet. Relat. Models, 1 (3), 405-414, 2008.
• with H. Guérin. On the uniqueness for the spatially homogeneous Boltzmann equation with a strong angular singularity. J. Stat. Phys., 131 (4), 749-781, 2008.
• Smoothness of the law of some 1d jumping SDEs with non-constant rate of jump. Electron. J. Probab., Vol. 13, 135-156, 2008.
• Uniqueness for a class of spatially homogeneous Boltzmann equations without angular cutoff. J. Stat. Phys., 125 (4), 927-946, 2006.
• A distance for coagulation. Markov Process. Related Fields, 12 (2), 399-406, 2006.
• Standard stochastic coalescence with sum kernels. Electron. Comm. Probab. 11, 141-148, 2006.
• On some stochastic coalescents. Probab. Theory Related Fields 136 (4), 509-523, 2006.
• with P. Laurencot. Well-posedness of Smoluchowski's coagulation equation for a class of homogeneous kernels. J. Funct. Anal., 233 (2), 351-379, 2006.
• with P. Laurencot. Local properties of self-similar solutions to Smoluchowski's equation with sum kernel. Proc. Roy. Soc. Edinburgh Sect. A 136 (3), 485-508, 2006.
• with J.S. Giet. Existence of densities for jumping SDEs. Stochastic Process. Appl., 116 (4), 643-661, 2006.
• with P. Laurencot. Existence of self-similar solutions to Smoluchowski's coagulation equation. Comm. Math. Phys., 256, (3), 589-609, 2005.
• with S. Mischler. A Boltzmann equation for elastic, inelastic, and coalescing collisions. J. Math. Pures Appl., 84 (9), 1173-1234, 2005.
• with S. Mischler. Exponential trend to equilibrium for discrete coagulation equations with strong fragmentation and without balance condition. Proc. R. Soc. Lond. Ser. A, Vol. 460, 2477-2486, 2004.
• with B. Roynette, E. Tanré. On long time behavior of some coagulation processes. Stochastic Process. Appl., 110, 1-17, 2004.
• with S. Mischler. On a discrete Boltzmann-Smoluchowski equation with rates bounded in the velocity variable. Commun. Math. Sci., 2, 55-63, 2004.
• with S. Méléard. A microscopic probabilistic description of a locally regulated population and macroscopic approximations. Ann. Appl. Probab. 14 (4), 1880-1919, 2004.
• with J.S. Giet. Exact simulation of nonlinear coagulation processes. Monte Carlo Methods Appl., 10 (2), 95-106, 2004.
• with J.S. Giet. Convergence of the Marcus-Lushnikov process. Methodol. Comput. Appl. Probab., 6, 219-231, 2004.
• with B. Roynette. On long time a.s. asymptotics of renormalized branching diffusion processes. Ann. Inst. H. Poincaré Probab. Statist., 39 (6), 979-991, 2003.
• with J.S. Giet. On small particles in coagulation-fragmentation equations. J. Statist. Phys., 111 (5/6), 1299-1329, 2003.
• with M. Deaconu, E. Tanré. Rate of convergence of a stochastic particle system associated with the Smoluchowski coagulation equation. Methodol. Comput. Appl. Probab., 5, 131-158, 2003.
• with M. Deaconu. Probabilistic approach of some discrete and continuous coagulation equations with diffusion. Stochastic Process. Appl., 101 (1), 83-111, 2002.
• Jumping SDEs: absolute continuity using monotonicity. Stochastic Process. Appl., 98 (2), 317-330, 2002.
• with S. Méléard. A weak criterion of absolute continuity for jump processes: application to the Boltzmann equation. Bernoulli, 8 (4), 537-558, 2002.
• with M. Deaconu, E. Tanré. A pure jump Markov process associated with Smoluchowski's coagulation equation. Ann. Probab., 30 (4), 1763-1796, 2002.
• Strict positivity of the density for simple jump processes using the tools of support theorems. Application to the Kac equation without cutoff. Ann. Probab. 30 (1), 135-170, 2002.
• with S. Méléard. A stochastic particle numerical method for 3D Boltzmann equations without cutoff. Math. Comp., 71, 583-604, 2002.
• with S. Méléard. A Markov process associated with a Boltzmann equation without cutoff and for non Maxwell molecules. J. Statist. Phys., 104 (1/2), 359-385, 2001.
• with S. Méléard. Monte Carlo approximations for 2D Boltzmann equations without cutoff and for non Maxwell molecules. Monte Carlo Methods Appl., 7 (1-2), 177-192, 2001.
• with S. Méléard. Monte Carlo approximations and fluctuations for 2D Boltzmann equations without cutoff. Markov Process. Related Fields, 7, 159-191, 2001.
• Strict positivity of a 2D spatially homogeneous Boltzmann equation without cutoff. Ann. Inst. H. Poincaré Probab. Statist., 37 (4), 481-502, 2001.
• Support theorem for the solution of a white-noise-driven driven parabolic SPDE with temporal Poissonian jumps. Bernoulli, 7 (1), 165-190, 2001.
• Strict positivity of a solution to a 1D Kac equation without cutoff. J. Statist. Phys., 99 (3/4), 725-749, 2000.
• Existence and regularity study for 2D Kac equation without cutoff by a probabilistic approach. Ann. Appl. Probab., 10 (2), 434-462, 2000.
• Malliavin calculus for parabolic SPDEs with jumps. Stochastic Process. Appl., 87, 115-147, 2000.
• Strict positivity of the density for a Poisson driven SDE. Stoch. Stoch. Reports, 68, 1-43, 1999.

Thèse, Paris 6, avec Sylvie Méléard, 1999. Calcul des variations stochastiques sur l'espace de Poisson, applications à des EDPS paraboliques avec sauts et à certaines équations de Boltzmann.
Hdr, Nancy, 2004. Etude d'équations différentielles stochastiques à sauts, d'équations de Boltzmann, de processus de coagulation-fragmentation, et de processus de branchement.