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Stochastic Partial Differential Equations

Comportement Asymptotique d'Équations à Dérivées Partielles Stochastiques
PhD Thesis, Univ. of Geneva (2001) Under the direction of J.-P. Eckmann
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Invariant Measures for Stochastic PDE's in Unbounded Domains
Written in collaboration with J.-P. Eckmann.
Nonlinearity 14 (2001), no 1, pp. 133-151 Link to published version
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Uniqueness of the Invariant Measure for a Stochastic PDE Driven by Degenerate Noise
Written in collaboration with J.-P. Eckmann.
Commun. Math. Phys. 219 (2001), no 3, pp. 523-565 Published version
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Exponential Mixing for a Stochastic PDE Driven by Degenerate Noise
Nonlinearity 15 (2002), no 2, pp. 271-279 Published version
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Exponential Mixing Properties of Stochastic PDEs Through Asymptotic Coupling
Probab. Theory Rel. Fields 124 (2002), no. 3, pp. 345-380 Published version
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Stationary solutions for a model of amorphous thin-film growth
Written in collaboration with D. Blömker.
Stochastic Analysis and Applications 22 (2004), no. 4, pp. 903-922 Published version
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Coupling stochastic PDEs
XIVth International Congress on Mathematical Physics (2005), pp. 281-289
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Amplitude Equations for SPDEs: Approximate Centre Manifolds and Invariant Measures
Written in collaboration with D. Blömker.
Proceedings of the IMA, (2004)
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Multiscale expansion of invariant measures for SPDEs
Written in collaboration with D. Blömker.
Commun. Math. Phys. 251 (2004), no 3, pp. 515-555 Published version
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Ergodicity of the 2D Navier-Stokes Equations with Degenerate Stochastic Forcing
Written in collaboration with J. Mattingly.
Annals of Maths 164 (2006), no 3, pp. 993-1032 Published version
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Modulation Equations: Stochastic Bifurcation in Large Domains
Written in collaboration with D. Blömker and G. Pavliotis.
Commun. Math. Phys. 258 (2005), no 2, pp. 479-512 Published version
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Malliavin calculus for highly degenerate 2D stochastic Navier-Stokes equations
Written in collaboration with J. Mattingly and E. Pardoux.
C. R. Acad. Sci. Paris, Ser. I 339 (2004), no. 11, pp. 793-796 Published version
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Ergodic properties of highly degenerate 2D stochastic Navier-Stokes equations
Written in collaboration with J. Mattingly.
C. R. Acad. Sci. Paris, Ser. I 339 (2004), no. 12, pp. 879-882 Published version
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Analysis of SPDEs Arising in Path Sampling Part I: The Gaussian Case
Written in collaboration with A. M. Stuart, J. Voß, and P. Wiberg.
Comm. Math. Sci. 3 (2005), no. 4, pp. 587-603 Published version
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Analysis of SPDEs Arising in Path Sampling Part II: The Nonlinear Case
Written in collaboration with A. M. Stuart and J. Voß.
Ann. Appl. Probab. 17 (2007), no. 5/6, pp. 1657-1706 Published version
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A Bayesian Approach to Data Assimilation
Written in collaboration with A. Apte, A. M. Stuart and J. Voß.
Physica D 230 (2007), pp.50-64 Published version
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Spectral gaps in Wasserstein distances and the 2D stochastic Navier-Stokes equations
Written in collaboration with J. Mattingly.
Ann. Probab. 36 (2008), no 6, pp. 2050-2091 Published version
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Multiscale Analysis for SPDEs with Quadratic Nonlinearities
Written in collaboration with D. Blömker and G. Pavliotis.
Nonlinearity 20 (2007), no. 7, pp. 1721-1744 Published version
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Sampling Conditioned Diffusions
Written in collaboration with A. M. Stuart and J. Voß.
In Trends in Stochastic Analysis, Cambridge University Press, vol. 353 of LMS Lecture Note Series (2009), pp. 159-186
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A Theory of Hypoellipticity and Unique Ergodicity for Semilinear Stochastic PDEs
Written in collaboration with J. Mattingly.
Electr. Journ. Probab. 16 (2011), pp. 658-738 Published version
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Signal Processing Problems on Function Space: Bayesian Formulation, Stochastic PDEs and Effective MCMC Methods
Written in collaboration with A. M. Stuart and J. Voß.
Preprint (2009)
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Sampling Conditioned Hypoelliptic Diffusions
Written in collaboration with A. M. Stuart and J. Voß.
Ann. Appl. Probab. 21 (2012), no. 2, pp. 669-698 Published version
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Hypoellipticity in Infinite Dimensions
Proceedings of ISAAC 09 (2009)
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Singular perturbations to semilinear stochastic heat equations
Probab. Theory Rel. Fields 152 (2012), no. 1-2, pp. 265-297 Published version
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Approximations to the Stochastic Burgers equation
Written in collaboration with J. Voß.
Journ. Nonlin. Sci. 12 (2011), no 6, pp. 897-920 Published version
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Rough Stochastic PDEs
Commun. Pure Appl. Math. 64 (2011), no 11, pp. 1547-1585 Published version
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Stochastic PDEs with multiscale structure
Written in collaboration with D. Kelly.
Electr. Journ. Probab. 17 (2012), no. 52, pp. 1-38 Published version
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A spatial version of the Itô-Stratonovich correction
Written in collaboration with J. Maas.
Ann. Probab. 40 (2012), no 4, pp. 1675-1714 Published version
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Rough Burgers-like equations with multiplicative noise
Written in collaboration with H. Weber.
Probab. Theory Rel. Fields 155 (2013), no. 1, pp. 71-126 Published version
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Solving the KPZ equation
Annals of Maths 178 (2013), no. 2, pp. 559-664 Published version
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Triviality of the 2D stochastic Allen-Cahn equation
Written in collaboration with H. Weber and M. Ryser.
Electr. Journ. Probab. 17 (2012), no. 39, pp. 1-14 Published version
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Approximating rough stochastic PDEs
Written in collaboration with J. Maas and H. Weber.
Commun. Pure Appl. Math. 67 (2014), no 5, pp. 776-870 Published version
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Random homogenisation of a highly oscillatory singular potential
Written in collaboration with E. Pardoux and A. Piatnitski.
SPDEs: Anal. Comp. 1 (2013), no. 4, pp. 571-605 Published version
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A theory of regularity structures
Invent. Math. 198 (2014), no. 2, pp. 269-504 Published version
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Introduction to Regularity Structures
Braz. Jour. Prob. Stat. 29 (2015), no. 2, pp. 175-210 Published version
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Singular stochastic PDEs
Proceedings of the ICM (2014)
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Large deviations for white-noise driven, nonlinear stochastic PDEs in two and three dimensions
Written in collaboration with H. Weber.
Ann. Fac. Sci. Toulouse Math. (6) 24 (2015), no. 1, pp. 55-92 Published version
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A Wong-Zakai theorem for stochastic PDEs
Written in collaboration with E. Pardoux.
J. Math. Soc. Japan 67 (2015), no. 4, pp. 1551-1604 Published version
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The dynamical sine-Gordon model
Written in collaboration with H. Shen.
Comm. Math. Phys. 341 (2016), no. 3, pp. 933-989 Published version
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A simple construction of the continuum parabolic Anderson model on R^2
Written in collaboration with C. Labbé.
Electron. Commun. Probab. 20 (2015), no. 43, 11 pp Published version
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Optimal rate of convergence for stochastic Burgers-type equations
Written in collaboration with K. Matetski.
Stoch. Partial Differ. Equ. Anal. Comput. 4 (2016), no. 2, pp. 402-437 Published version
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Multiplicative stochastic heat equations on the whole space
Written in collaboration with C. Labbé.
Preprint (2015)
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A central limit theorem for the KPZ equation
Written in collaboration with H. Shen.
Preprint (2015)
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Discretisations of rough stochastic PDEs
Written in collaboration with K. Matetski.
Preprint (2015)
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A class of growth models rescaling to KPZ
Written in collaboration with J. Quastel.
Preprint (2015)
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Large scale behaviour of 3D phase coexistence models
Written in collaboration with W. Xu.
Preprint (2016)
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The motion of a random string
Preprint (2016)
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The reconstruction theorem in Besov spaces
Written in collaboration with C. Labbé.
Preprint (2016)
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The strong Feller property for singular stochastic PDEs
Written in collaboration with J. Mattingly.
Preprint (2016)
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