Thèmes de recherche

Publications

• Sandra Cerrai, Arnaud Debussche. Large deviations for the two-dimensional stochastic Navier-Stokes equation with vanishing noise correlation, Annales de l'IHP, Proba-Stat, to appear (2018). PDF
• Arnaud Debussche, Charles-Edouard Bréhier. Kolmogorov equations and weak order analysis for SPDEs with nonlinear diffusion coefficient, Journal de Math. Pures et Appl., to appear (2018). PDF
• Arnaud Debussche, Hendrik Weber. The Schrödinger equation with spatial white noise potential, Electronic Journal of Probability, Vol. 23, pp. 1-16 (2018). PDF
• Sandra Cerrai, Arnaud Debussche. Large deviations for the dynamic Φ^{2n}_d model, Applied Mathematics and Optimization. (2018). PDF

• Arnaud Debussche, Giuseppe Da Prato. An integral inequality for the invariant measure of a stochastic reaction-diffusion equation, Journal of Evolution Equations, 17, 1, pp. 197-214 (2017). PDF
• Anne de Bouard, Arnaud Debussche, Reika Fukuizumi, Romain Poncet. Fluctuations and temperature effects in Bose-Einstein condensation, ESAIM: proceedings and surveys, A paraitre (2017). PDF
• Arnaud Debussche, Julien Vovelle. Approximation - diffusion in stochastically forced kinetic equations, Prepublication (2017). PDF
• Arnaud Debussche, Jörg Martin. Solution to the stochastic Schrödinger equation on the full space, Prepublication (2017). PDF
• Anne de Bouard, Arnaud Debussche, Reika Fukuizumi. Long time behavior of GP equation at positive temperature, Prepublication (2017). PDF
• Arnaud Debussche, Mac Jugal Nguepedja Nankep. A law of large number in the supremum norm for a multi scale stochastic spatial gene network, Prepublication (2017). PDF

• Arnaud Debussche, Martina Hofmanova, Julien Vovelle. Degenerate Parabolic Stochastic Partial Differential Equations: Quasilinear case, Annals of Probability, 44, 3, pp. 1916-1955 (2016). PDF
• Arnaud Debussche, Sylvain De Moor, Julien Vovelle. Diffusion limit for the radiative transfer equation perturbed by a Markovian process, Asymptotic Analysis, vol. 98, no. 1-2, pp. 31-58 (2016). PDF
• Giuseppe Da Prato, Arnaud Debussche. Estimate for P_tD for the stochastic Burgers equation, Annales de l'IHP, Proba-Stat, Vol. 52, No 3, pp. 1248-1258 (2016). PDF
• Ismael Bailleul, Arnaud Debussche, Martina Hofmanova. Quasilinear generalized parabolic Anderson model equation, Prepublication (2016). PDF

• Arnaud Debussche, Julien Vovelle. Invariant measure of scalar first-order conservation laws with stochastic forcing, Probability Theory and Related Fields, 163, 3, pp. 575-611 (2015). PDF
• Radoin Belaouar, Anne de Bouard, Arnaud Debussche. Numerical analysis of the nonlinear Schrödinger equation with white noise dispersion, Stochastic Partial Differential Equations: Analysis and Computations, 3, 1, pp. 103-132 (2015). PDF
• Arnaud Debussche, Sylvain De Moor, Martina Hofmanova. A regularity result for quasilinear stochastic partial differential equations of parabolic type, SIAM Journal on Mathematical Analysis, 47, 2, pp. 1590-1614 (2015). PDF
• Arnaud Debussche, Sylvain De Moor, Julien Vovelle. Diffusion limit for the radiative transfer equation perturbed by a Wiener process, Kinetic and Related Models, 8, 3, pp. 467-492 (2015). PDF

• Arnaud Debussche, Marco Romito. Existence of densities for the 3D Navier--Stokes equations driven by Gaussian noise, Probability Theory and Related Fields, 158, 3-4, pp. 575-596 (2014). PDF
• Giuseppe Da Prato, Arnaud Debussche. Existence of the Fomin derivative of the invariant measure of a stochastic reaction--diffusion equation, Proceeding du RIMS Workshop on Mathematical Analysis of Viscous Incompressible Fluid, Kyoto (2014). PDF

• Arnaud Debussche. Ergodicity results for the stochastic Navier-Stokes equations: an introduction, Lecture Notes in Math., Springer, Heidelberg, 2073, pp. 23-108 (2013). PDF
• Arnaud Debussche, Michael Hogele, Peter Imkeller. The dynamics of nonlinear reaction-diffusion equations with small heavy-tailed Lévy noise, Lecture Notes in Mathematics, Springer Verlag, 2085 (2013). PDF
• Arnaud Debussche, Nicolas Fournier. Existence of densities for stable-like driven SDE's with Hölder continuous coefficients., Journal of Functional Analysis, 264, 8, pp. 1757-1778 (2013). PDF
• Julia Charrier, Arnaud Debussche. Weak truncation error estimates for elliptic PDEs with lognormal coefficients, Stochastic Partial Differential Equations: Analysis and Computations, 1, 1, pp. 63-93 (2013). PDF
• Arnaud Debussche, Julien Vovelle. Scalar conservation laws with stochastic forcing, revised version, Prepublication (2013). PDF

• Sergio Albeverio, Arnaud Debussche, Lihu Xu. Exponential mixing of the 3D stochastic Navier-Stokes equations driven by mildly degenerate noises, Applied Mathematics and Optimization journal, 66, 2, pp. 273-308 (2012). PDF
• Alina Crudu, Arnaud Debussche, Aurélie Muller, Ovidiu Radulescu. Convergence of stochastic gene networks to hybrid piecewise deterministic processes, The Annals of Applied Prob., 22, 5, pp. 1822-1859 (2012). [DOI] PDF
• Arnaud Debussche, Julien Vovelle. Diffusion limit for a stochastic kinetic problem, Commun. Pure Appl. Anal., 11, 6, pp. 2305-2326 (2012). 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, Nonlinearity, 25 (2012). PDF
• Arnaud Debussche, Erwan Faou. Weak backward error analysis for SDEs, SIAM Journal on Numerical Analysis, 43, 3, pp. 1735-1752 (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, Ludovic Goudenege. 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, Ying Hu, Gianmario Tessitore. Ergodic BSDEs under weak dissipative assumptions, Stochastic Processes and Applications, 121, 3, pp. 407-426 (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
• 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, 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. 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

• Arnaud Debussche, Jacques Printems. Weak order for the discretization of the stochastic heat equation, Math of Comp, 78, 266, pp. 845-863 (2009). 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
• Alina Crudu, Arnaud Debussche, Ovidiu Radulescu. Hybrid stochastic simplifications for multiscale gene networks, BMC Systems Biology, 3:89 (2009).
• Anne de Bouard, Arnaud Debussche. On a stochastic Korteweg-de Vries equation with homogeneous noise, Sémin. équ. Dériv. Partielles, Ecole Polytech. (2009).

• 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, Eric 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, Luciano Tubaro. A modified Kardar-Parisi-Zhang model, Electron. Comm. Probab., 12, pp. 442-453 (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
• 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
• 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
• Giuseppe Da Prato, Arnaud Debussche. m-dissipativity of Kolmogorov operators corresponding to Burgers equations, Potential Analysis, 26, 1, pp. 31-55 (2007). 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. 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. 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
• 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).
• 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).
• 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).

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