Arnaud Debussche ENS Cachan, Antenne de Bretagne Avenue Robert Schumann 35170 BRUZ Directeur du Département de Mathématiques de l'ENS Cachan Bretagne. Membre Junior de l'Institut Universitaire de France. IRMAR, équipes d'Analyse Numérique et de Processus Stochastiques.         02.99.05.93.11   Bâtiment A. Sauvy (RDC)         02.99.05.93.28 @

Thèmes de recherche

Publications

Divers

Enseignement

Curriculum Vitæ

Thèmes de recherche

Publications

• Arnaud Debussche, Marco Romito. Existence of densities for the 3D Navier--Stokes equations driven by Gaussian noise, Prepublication (2012). PDF

• Arnaud Debussche. Weak approximation of stochastic partial differential equations: the nonlinear case, Math of Comp, 80, pp. 89-117 (2011). PDF
• Arnaud Debussche. Ergodicity results for the stochastic Navier-Stokes equations: an introduction, Prepublication (2011). PDF
• Arnaud Debussche, Ludovic Goudenège. Stochastic Cahn-Hilliard equation with double singular nonlinearities and two reflections, SIAM Journal on Mathematical Analysis, 43, 3, pp. 1473-1494 (2011). PDF
• Arnaud Debussche, Yoshio Tsustumi. 1D quintic nonlinear equation with white noise dispersion, Journal de Mathématiques Pures et Appliquées, 96, pp. 363-376 (2011). PDF
• Arnaud Debussche, Julien Vovelle. Diffusion limit for a stochastic kinetic problem, Prepublication (2011). PDF
• Arnaud Debussche, Erwan Faou. Weak backward error analysis for SDEs, Prepublication (2011). PDF
• Arnaud Debussche, Ying Hu, Gianmario Tessitore. Ergodic BSDEs under weak dissipative assumptions, Stochastic Processes and Applications, 121, 3, pp. 407-426 (2011). PDF
• Arnaud Debussche, Michael Hogele, Peter Imkeller. Asymptotic first exit times of the Chafee-Infante equation with small heavy tailed noise, Electronic Communications in Probability, 16, pp. 213-225 (2011). PDF
• Arnaud Debussche, Nathan Glatt-Holtz, Roger Temam. Local Martingale and Pathwise Solutions for an Abstract Fluids Model, Physica D, 14-15, pp. 1123-1144 (2011). PDF
• Alina Crudu, Arnaud Debussche, Aurélie Muller, Ovidiu Radulescu. Convergence of stochastic gene networks to hybrid piecewise deterministic processes, Annals of Applied Prob., A paraitre (2011). PDF
• Arnaud Debussche, Nathan Glatt-Holtz, Roger Temam, Mohammed Ziane. Global existence and regularity for the 3D stochastic primitive equations of the ocean and atmosphere with multiplicative white noise, Prepublication (2011). PDF

• Arnaud Debussche, Julien Vovelle. Scalar conservation laws with stochastic forcing, Journal of Functional Analysis, 259, pp. 1014-1042 (2010). PDF
• Giuseppe Da Prato, Arnaud Debussche. Asymptotic behavior of stochastic PDEs with random coefficients, Discrete and Continuous Dynamical Systems, Series A, 27, 4, pp. 1553-1570 (2010). PDF
• Anne de Bouard, Arnaud Debussche. The nonlinear Schrodinger equation with white noise dispersion, Journal of Functional Analysis, 259, pp. 1300-1321 (2010). PDF
• Sergio Albeverio, Arnaud Debussche, Lihu Xu. Exponential mixing of the 3D stochastic Navier-Stokes equations driven by mildly degenerate noises, Prepublication (2010). PDF

• Arnaud Debussche, Julien Vovelle. Long-time behavior in scalar conservation laws, Diff. and Int. Eq., 22, 3-4, pp. 225-238 (2009). PDF
• Arnaud Debussche, Erwan Faou. Modified energy for split-step methods applied to the linear Schrödinger equation, SIAM Journal on numerical analysis, 47, 5, pp. 3705-3719 (2009). PDF
• Anne de Bouard, Arnaud Debussche. Soliton dynamics for the Korteweg-de Vries equation with multiplicative homogeneous noise, Electron. Journ. Probab., 14, 58, pp. 1727-1744 (2009). PDF
• Anne de Bouard, Arnaud Debussche. On a stochastic Korteweg-de Vries equation with homogeneous noise, Sémin. Équ. Dériv. Partielles, École Polytech. (2009).
• Arnaud Debussche, Jacques Printems. Weak order for the discretization of the stochastic heat equation, Math of Comp, 78, 266, pp. 845-863 (2009). PDF
• Alina Crudu, Arnaud Debussche, Ovidiu Radulescu. Hybrid stochastic simplifications for multiscale gene networks, BMC Systems Biology, 3:89 (2009).

• Arnaud Debussche, Éric Gautier. Small noise asymptotic of the timing jitter in soliton transmission, The Annals of Applied Probability, 18, 1, pp. 178-208 (2008). PDF
• Giuseppe Da Prato, Arnaud Debussche. On the martingale probem associated to the 2D and 3D Stochastic Navier-Stokes equations, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 19, 3, pp. 247-264 (2008). PDF
• Giuseppe Da Prato, Arnaud Debussche. 2D Stochastic Navier-Stokes equations with a time-periodic forcing term, Journal of Dynamics and Differential Equations, 20, 2, pp. 301-335 (2008). PDF

• Arnaud Debussche, Lorenzo Zambotti. Conservative Stochastic Cahn-Hilliard equation with reflection, Annals of Probability, 35, 5, pp. 1706-1739 (2007). PDF
• Anne de Bouard, Arnaud Debussche. Random modulation of solitons for the stochastic Korteweg-de Vries equation, Annales de IHP, Analyse non lineair, 24, 2, pp. 251-278 (2007). PDF
• Anne de Bouard, Arnaud Debussche. The Korteweg-de Vries equation with multiplicative homogeneous noise, "Stochastic Differential Equations---Theory and Applications" in honor of Professor Boris Rozovskii. P. Baxendale and S. Lototsky editors, World Scientific (2007). PDF
• Giuseppe Da Prato, Arnaud Debussche. m-dissipativity of Kolmogorov operators corresponding to Burgers equations, Potential Analysis, 26, 1, pp. 31-55 (2007). PDF
• Giuseppe Da Prato, Arnaud Debussche, Luciano Tubaro. A modified Kardar-Parisi-Zhang model, Electron. Comm. Probab., 12, pp. 442-453 (2007). PDF
• Arnaud Debussche, Marco Fuhrman, Gianmario Tessitore. Optimal Control of a Stochastic Heat Equation with Boundary-noise and Boundary-control, ESAIM Control, Optimisation and Calculus of Variations, 13, 1, pp. 178-205 (2007). PDF

• Anne de Bouard, Arnaud Debussche. Weak and strong order of convergence of a semi discrete scheme for the stochastic Nonlinear Schrödinger equation, Applied Mathematics and Optimization journal, 54, 3, pp. 369-399 (2006). PDF
• Arnaud Debussche, Jacques Printems. Convergence of a semi-discrete scheme for the stochastic Korteweg--de Vries equation, Discrete and Continuous Dynamical Systems B, 6, 4, pp. 761-781 (2006). PDF
• Arnaud Debussche, Cyril Odasso. Markov solutions for the 3D stochastic Navier--Stokes equations with state dependent noise, Journal of Evolution Equations, 6, 2, pp. 305-324 (2006). PDF

• Anne de Bouard, Arnaud Debussche. Blow-up for the supercritical stochastic nonlinear Schrödinger equation with multiplicative noise, Annals of Probability, 33, 3, pp. 1078-1110 (2005).
• Arnaud Debussche, Cyril Odasso. Ergodicity for a weakly damped stochastic Nonlinear Schrödinger equation, Journal of Evolution Equations, 5, 3, pp. 317-356 (2005). PDF
• Giuseppe Da Prato, Arnaud Debussche, Luciano Tubaro. Coupling for some partial differential equations driven by white noise, Stoch. Proc. and Appl., 115, 8, pp. 1384-1407 (2005). PDF
• Arnaud Debussche, Jacques Laminie, Ezzedine Zahrouni. A dynamical multilevel scheme for the Burgers equation: wavelet and hierarchical finite element, Journal of Scientific Computing, 25, 3, pp. 445-497 (2005).
• Marc Barton-Smith, Arnaud Debussche, Laurent DiMenza. Numerical study of two dimensional stochastic NLS equations, Numerical Methods for Partial Differential Equations, 21, 4, pp. 810-842 (2005).

Divers

Enseignement

Curriculum Vitæ

ENS Cachan, Antenne de Bretagne - Campus de Ker Lann - Avenue Robert Schuman - 35170 BRUZ