Nicolas Fournier,

professeur au LPMA.

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 M1 Processus de sauts.
Des sujets d'examen : 2015-Session 1 Corrigé 2016-Session 1 Corrigé

S. Delattre, N. Fournier. On Monte-Carlo tree search algorithm for deterministic games with alternate moves and complete information.

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

N. Fournier, L. Xu. On the equivalence between some jumping SDEs with rough coefficients and some non-local PDEs.

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. Accepté aux Ann. Appl. Probab.

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.