Nicolas Fournier,

professeur au LPSM.

Couloir 16-26, bureau 219.

Tél : 01 44 27 70 42.

nicolas.fournier@upmc.fr

Polycopié du cours de M2 Compléments de probabilités.

Polycopié du cours de M2 Calcul Stochastique, Exercices.

Polycopié du cours de M1 Processus de sauts. Des sujets d'examen : 2016-Session 1, Corrigé, 2017-Session 1, Corrigé.

N. Fournier, C. Tardif. One-dimensional critical kinetic Fokker-Planck equations, Bessel and Stable processes.

N. Fournier, E. Tanré, R. Veltz. On a toy network of neurons interacting through their dendrites.

S. Delattre, N. Fournier. On Monte-Carlo tree search for deterministic games with alternate moves and complete information. Accepté à ESAIM P&S. Code

N. Fournier. A recursive algorithm and a series expansion related to the homogeneous Boltzmann equation for hard potentials with angular cutoff. Accepté à Kinet. Relat. Models.

N. Fournier, L. Xu. On the equivalence between some jumping SDEs with rough coefficients and some non-local PDEs. Accepté aux Ann. Inst. H. Poincaré Probab. Statist.

S. Delattre, N. Fournier. On the Kozachenko-Leonenko entropy estimator. J. Statist. Plann. Inference, Vol. 185, 69-93, 2017.

N. Fournier, 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.

N. Fournier, 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.

S. Delattre, N. Fournier. Statistical inference versus mean field limit for Hawkes processes. Electron. J. Stat., Vol. 10, 1223-1295, 2016.

N. Fournier, M. Hauray. Propagation of chaos for the Landau equation with moderately soft potentials. Ann. Probab., Vol. 44, 3581-3660, 2016.

N. Fournier, E. Löcherbach. On a toy model of interacting neurons. Ann. Inst. H. Poincaré Probab. Statist., Vol. 52, 1844-1876, 2016.

S. Delattre, N. Fournier, M. Hoffmann. Hawkes processes on large networks. Ann. Appl. Probab., Vol. 26, 216-261, 2016.

N. Fournier, S. Mischler. Rate of convergence of the Nanbu particle system for hard potentials. Ann. Probab., Vol. 44, 589-627, 2016.

N. Fournier, A. Guillin. On the rate of convergence in Wasserstein distance of the empirical measure. Probab. Theory Related Fields, Vol. 162, 707-738, 2015.

N. Fournier. Finiteness of entropy for the homogeneous Boltzmann equation with measure initial condition. Ann. Appl. Probab., Vol. 25, No 2, 860-897, 2015.

X. Bressaud, N. Fournier. 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.

N. Fournier, M. Hauray, S. Mischler. Propagation of chaos for the 2D viscous vortex model. J. Eur. Math. Soc., Vol. 16, No 7, 1423-1466, 2014.

X. Bressaud, N. Fournier. One-dimensional general forest fire processes. Mém. Soc. Math. Fr., Vol. 132, vi+138 pages, 2013.

A. Debussche, N. Fournier. Existence of densities for stable-like driven SDE's with Hölder continuous coefficients. J. Funct. Anal., Vol. 264, No 8, 1757-1778, 2013.

N. Fournier. On pathwise uniqueness for stochastic differential equations driven by stable Lévy processes. Ann. Inst. H. Poincaré Probab. Statist., Vol. 49, 138-159, 2013.

N. Fournier, D. Godinho. Asymptotics of grazing collisions and particle approximation for the Kac equation without cutoff. Comm. Math. Phys., Vol. 316, 307-344, 2012.

E. Cepeda, N. Fournier. Smoluchowski's coagulation equation: rate of convergence of the Marcus-Lushnikov process. Stochastic Process. Appl., Vol. 121, Issue 6, 1411-1444, 2011.

N. Fournier, J. Printems. Stability of the stochastic heat equation in L1([0,1]). Electron. Comm. Probab., Vol. 16, 337-352, 2011.

V. Bally, N. Fournier. Regularization properties of the 2D homogeneous Boltzmann equation without cutoff. Probab. Theory Related Fields, Vol. 151, no 3-4, 659-704, 2011.

N. Fournier. Simulation and approximation of Lévy-driven stochastic differential equations. ESAIM P&S, Vol. 15, 249-269, 2011.

N. Fournier. Uniqueness of bounded solutions for the homogeneous Landau equation with a Coulomb potential. Comm. Math. Phys., Vol. 299, no 3, 765-782, 2010.

J. Barral, N. Fournier, S. Jaffard, S. Seuret. A pure jump Markov process with a random singularity spectrum. Ann. Probab., Vol. 38, no 5, 1924-1946, 2010.

X. Bressaud, N. Fournier. Asymptotics of one-dimensional forest fire processes. Ann. Probab., Vol. 38, no 5, 1783-1816, 2010.

N. Fournier, J. Printems. Absolute continuity of some one-dimensional processes. Bernoulli, Vol. 16, 2, 343-360, 2010.

N. Fournier. Particle approximation of some Landau equations. Kinet. Relat. Models, Vol. 2, 3, 451 - 464, 2009.

N. Fournier, 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.

N. Fournier, H. Guérin. Well-posedness of the spatially homogeneous Landau equation for soft potentials. J. Funct. Anal., Volume 256, 9, 2542-2560, 2009.

X. Bressaud, N. Fournier. On the invariant distribution of an avalanche process. Ann. Probab., Volume 37, No 1, Pages 48-77, 2009.

N. Fournier, P. Laurencot. Marcus Lushnikov processes, Smoluchowski's and Flory's models. Stochastic Process. Appl., Volume 119, Issue 1, Pages 167-189, 2009.

N. Fournier, E. Löcherbach. Stochastic coalescence with homogeneous-like interaction rates. Stochastic Process. Appl., Volume 119, Issue 1, Pages 45-73, 2009.

N. Fournier. A new regularization possibility for the Boltzmann equation with soft potentials. Kinet. Relat. Models, 1 (3), 405-414, 2008.

N. Fournier, H. Guérin. On the uniqueness for the spatially homogeneous Boltzmann equation with a strong angular singularity. J. Stat. Phys., 131 (4), 749-781, 2008.

N. Fournier. Smoothness of the law of some 1d jumping SDEs with non-constant rate of jump. Electron. J. Probab., Vol. 13, 135-156, 2008.

N. Fournier. Uniqueness for a class of spatially homogeneous Boltzmann equations without angular cutoff. J. Stat. Phys., 125 (4), 927-946, 2006.

N. Fournier. A distance for coagulation. Markov Process. Related Fields, 12 (2), 399-406, 2006.

N. Fournier. Standard stochastic coalescence with sum kernels. Electron. Comm. Probab. 11, 141-148, 2006.

N. Fournier. On some stochastic coalescents. Probab. Theory Related Fields 136 (4), 509-523, 2006.

N. Fournier, P. Laurencot. Well-posedness of Smoluchowski's coagulation equation for a class of homogeneous kernels. J. Funct. Anal., 233 (2), 351-379, 2006.

N. Fournier, 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.

N. Fournier, J.S. Giet. Existence of densities for jumping SDEs. Stochastic Process. Appl., 116 (4), 643-661, 2006.

N. Fournier, P. Laurencot. Existence of self-similar solutions to Smoluchowski's coagulation equation. Comm. Math. Phys., 256, (3), 589-609, 2005.

N. Fournier, S. Mischler. A Boltzmann equation for elastic, inelastic, and coalescing collisions. J. Math. Pures Appl., 84 (9), 1173-1234, 2005.

N. Fournier, 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.

N. Fournier, B. Roynette, E. Tanré. On long time behavior of some coagulation processes. Stochastic Process. Appl., 110, 1-17, 2004.

N. Fournier, S. Mischler. On a discrete Boltzmann-Smoluchowski equation with rates bounded in the velocity variable. Commun. Math. Sci., Supplemental issue 1, 2004.

N. Fournier, S. Méléard. A microscopic probabilistic description of a locally regulated population and macroscopic approximations. Ann. Appl. Probab. 14 (4), 1880-1919, 2004.

N. Fournier, J.S. Giet. Exact simulation of nonlinear coagulation processes. Monte Carlo Methods Appl., 10 (2), 95-106, 2004.

N. Fournier, J.S. Giet. Convergence of the Marcus-Lushnikov process. Methodol. Comput. Appl. Probab., 6, 219-231, 2004.

N. Fournier, B. Roynette. On long time a.s. asymptotics of renormalized branching diffusion processes. Ann. Inst. H. Poincaré Probab. Statist., 39 (6), 979-991, 2003.

N. Fournier, J.S. Giet. On small particles in coagulation-fragmentation equations. J. Statist. Phys., 111 (5/6), 1299-1329, 2003.

M. Deaconu, N. Fournier, E. Tanré. Rate of convergence of a stochastic particle system associated with the Smoluchowski coagulation equation. Methodol. Comput. Appl. Probab., 5, 131-158, 2003.

M. Deaconu, N. Fournier. Probabilistic approach of some discrete and continuous coagulation equations with diffusion. Stochastic Process. Appl., 101 (1), 83-111, 2002.

N. Fournier. Jumping SDEs: absolute continuity using monotonicity. Stochastic Process. Appl., 98 (2), 317-330, 2002.

N. Fournier, S. Méléard. A weak criterion of absolute continuity for jump processes: application to the Boltzmann equation. Bernoulli, 8 (4), 537-558, 2002.

M. Deaconu, N. Fournier, E. Tanré. A pure jump Markov process associated with Smoluchowski's coagulation equation. Ann. Probab., 30 (4), 1763-1796, 2002.

N. Fournier. 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.

N. Fournier, S. Méléard. A stochastic particle numerical method for 3D Boltzmann equations without cutoff. Math. Comp., 71, 583-604, 2002.

N. Fournier, 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.

N. Fournier, 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.

N. Fournier, S. Méléard. Monte Carlo approximations and fluctuations for 2D Boltzmann equations without cutoff. Markov Process. Related Fields, 7, 159-191, 2001.

N. Fournier. Strict positivity of a 2D spatially homogeneous Boltzmann equation without cutoff. Ann. Inst. H. Poincaré Probab. Statist., 37 (4), 481-502, 2001.

N. Fournier. Support theorem for the solution of a white-noise-driven driven parabolic SPDE with temporal Poissonian jumps. Bernoulli, 7 (1), 165-190, 2001.

N. Fournier. Strict positivity of a solution to a 1D Kac equation without cutoff. J. Statist. Phys., 99 (3/4), 725-749, 2000.

N. Fournier. Existence and regularity study for 2D Kac equation without cutoff by a probabilistic approach. Ann. Appl. Probab., 10 (2), 434-462, 2000.

N. Fournier. Malliavin calculus for parabolic SPDEs with jumps. Stochastic Process. Appl., 87, 115-147, 2000.

N. Fournier. 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.