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hal-00948570v1  Article dans une revue
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, 2015, 3 (1), pp.103-132. <10.1007/s40072-015-0044-z>
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hal-01481966v1  Pré-publication, Document de travail
Charles-Edouard Bréhier, Arnaud Debussche. Kolmogorov Equations and Weak Order Analysis for SPDES with Nonlinear Diffusion Coefficient
2017-22. 2017
hal-01297401v1  Article dans une revue
Alexey Chernov, Arnaud Debussche, Fabio Nobile. Numerical methods for random and stochastic partial differential equations
Stochastics and Partial Differential Equations Analysis and Computations, 2016, 4 (1), pp.1-2. <10.1007/s40072-016-0073-2>
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hal-01518465v1  Pré-publication, Document de travail
Sandra Cerrai, Arnaud Debussche. Large deviations for the dynamic $\Phi^{2n}_d$ model
2017
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hal-01411205v1  Pré-publication, Document de travail
Arnaud Debussche, Hendrik Weber. The Schrödinger equation with spatial white noise potential
2016-155. 2016
hal-01126707v1  Communication dans un congrès
Giuseppe Da Prato, Arnaud Debussche. Existence of the Fomin derivative of the invariant measure of a stochastic reaction--diffusion equation
Toshiaki Hishida; Yoshihiro Shibata. RIMS Workshop on Mathematical analysis of viscous incompressible fluid, Nov 2014, Kyoto, Japan. 2014
hal-01110454v1  Article dans une revue
Giuseppe Da Prato, Arnaud Debussche. Estimate for $P_tD$ for the stochastic Burgers equation
Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institute Henri Poincaré, 2016, 52 (3), pp.1248-1258. <10.1214/15-AIHP685>
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hal-00460976v1  Article dans une revue
Giuseppe Da Prato, Arnaud Debussche. Asymptotic behavior of stochastic PDEs with random coefficients
Discrete and Continuous Dynamical Systems - Series S, American Institute of Mathematical Sciences, 2010, 27 (4), pp.1553-1570. <10.3934/dcds.2010.27.1553>
hal-00383241v1  Article dans une revue
Giuseppe Da Prato, Arnaud Debussche. 2D Stochastic Navier–Stokes Equations with a Time-Periodic Forcing Term
Journal of Dynamics and Differential Equations, Springer Verlag, 2008, 20 (2), pp.301-335. <10.1007/s10884-007-9074-1>
hal-00730709v1  Article dans une revue
Jacques Laminie, Caterina Calgaro, Arnaud Debussche. On a multilevel approach for the two-dimensional Navier-Stokes equations with finite elements.
International Journal for Numerical Methods in Fluids, Wiley, 1998, 27 (1-4), pp.241-258
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hal-00527508v1  Article dans une revue
Arnaud Debussche, Yoshio Tsutsumi. 1D quintic nonlinear Schrödinger equation with white noise dispersion
Journal de Mathématiques Pures et Appliquées, Elsevier, 2011, 96 (4), pp.363-376. <10.1016/j.matpur.2011.02.002>
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hal-00278737v1  Article dans une revue
Giuseppe Da Prato, Arnaud Debussche. On the martingale probem associated to the $2D$ and $3D$ Stochastic Navier-Stokes equations
Rendiconti Lincei - Matematica E Applicationi, 2008, 19 (3), pp.247-264
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hal-00003102v1  Article dans une revue
Giuseppe Da Prato, Arnaud Debussche, Luciano Tubaro. Coupling for some partial differential equations driven by white noise
Stochastic Processes and their Applications, Elsevier, 2005, 115 (8), pp.1384-1407. <10.1016/j.spa.2005.03.010>
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hal-00472146v1  Article dans une revue
Arnaud Debussche, Ying Hu, Gianmario Tessitore. Ergodic BSDEs under weak dissipative assumptions
Stochastic Processes and their Applications, Elsevier, 2011, 121 (3), pp.407-426. <10.1016/j.spa.2010.11.009>
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hal-00553482v1  Article dans une revue
Alina Crudu, Arnaud Debussche, Aurélie Muller, Ovidiu Radulescu. Convergence of stochastic gene networks to hybrid piecewise deterministic processes
Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2012, 22 (5), pp.1822-1859. <10.1214/11-AAP814>
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hal-00019026v1  Article dans une revue
Arnaud Debussche, Eric Gautier. Small noise asymptotic of the timing jitter in soliton transmission
The Annals of Applied Probability : an official journal of the institute of mathematical statistics, The Institute of Mathematical Statistics, 2008, 18 (1), pp.178-208. <10.1214/07-AAP449>
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hal-00183249v1  Article dans une revue
Arnaud Debussche, Jacques Printems. Weak order for the discretization of the stochastic heat equation.
Mathematics of Computation / Mathematics of Computation, American Mathematical Society, 2009, 78 (266), pp.845-863
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hal-00271302v1  Article dans une revue
Arnaud Debussche. Weak approximation of stochastic partial differential equations: the non linear case
Mathematics of Computation / Mathematics of Computation, American Mathematical Society, 2011, 80 (273), pp.89-117
hal-00457283v1  Communication dans un congrès
Anne De Bouard, Arnaud Debussche. On a stochastic Korteweg-de Vries equation with homogeneous noise
Séminaire Équations aux Dérivées Partielles, École Polytechnique, 2009, Palaiseau, France
hal-00947868v1  Ouvrage (y compris édition critique et traduction)
Arnaud Debussche, Michael Högele, Peter Imkeller. The dynamics of nonlinear reaction-diffusion equations with small Lévy noise
Springer, xiii-163 p., 2013, Lecture notes in mathematics n° 2085, 978-3-319-00827-1. <10.1007/978-3-319-00828-8>
hal-00383307v1  Chapitre d'ouvrage
Anne De Bouard, Arnaud Debussche. The Korteweg-de Vries equation with multiplicative homogeneous noise
Peter H. Baxendale ; Sergey V. Lototsky. Stochastic differential equations: theory and applications, World Scientific Publishing Co, pp.113-133, 2007, Interdisciplinary Mathematical Sciences
hal-00383314v1  Article dans une revue
Anne De Bouard, Arnaud Debussche. Weak and Strong Order of Convergence of a Semidiscrete Scheme for the Stochastic Nonlinear Schrodinger Equation
Applied Mathematics and Optimization, Springer Verlag (Germany), 2006, 54 (3), pp.369-399. <10.1007/s00245-006-0875-0>
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hal-00463793v1  Article dans une revue
Sergio Albeverio, Arnaud Debussche, Lihu Xu. Exponential mixing of the 3D stochastic Navier-Stokes equations driven by mildly degenerate noises
Applied Mathematics and Optimization, Springer Verlag (Germany), 2012, 66 (2), pp.273-308. <10.1007/s00245-012-9172-2>
hal-00457292v1  Article dans une revue
Arnaud Debussche, Lorenzo Zambotti. Conservative Stochastic Cahn-Hilliard equation with reflection
Annals of Probability, Institute of Mathematical Statistics, 2007, 35 (5), pp.1706-1739. <10.1214/009117906000000773>
hal-00383396v1  Article dans une revue
Anne De Bouard, Arnaud Debussche. Blow-up for the stochastic nonlinear Schrödinger equation with multiplicative noise
Annals of Probability, Institute of Mathematical Statistics, 2005, 33 (3), pp.1078-1110. <10.1214/009117904000000964>
hal-00365095v1  Article dans une revue
Giuseppe Da Prato, Arnaud Debussche, Luciano Tubaro. A modified Kardar-Parisi-Zhang model
Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2007, 12, pp.442-453
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hal-00553477v1  Article dans une revue
Arnaud Debussche, Michael Högele, Peter Imkeller. Asymptotic first exit times of the Chafee-Infante equation with small heavy-tailed Lévy noise
Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2011, 16, pp.213-225. <10.1214/ECP.v16-1622>
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hal-00348221v1  Article dans une revue
Arnaud Debussche, Erwan Faou. Modified energy for split-step methods applied to the linear Schrödinger equation
SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2009, 47 (5), pp.3705-3719
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