Stochastic Partial Differential Equations

This list has been taken from SPDEs at https://www.hairer.org/ which remains the reference link.

• Comportement Asymptotique d’Équations à Dérivées Partielles Stochastiques
  PhD Thesis, Univ. of Geneva (2001) Under the direction of J.-P. Eckmann – PDF File
• Invariant Measures for Stochastic PDE’s in Unbounded Domains
  Written in collaboration with J.-P. Eckmann.
  Nonlinearity 14 (2001), no 1, pp. 133-151
  Published version – PDF File
• 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
  PDF File
• Exponential Mixing for a Stochastic PDE Driven by Degenerate Noise
  Nonlinearity 15 (2002), no 2, pp. 271-279
  Published version – PDF File
• Exponential Mixing Properties of Stochastic PDEs Through Asymptotic Coupling
  Probab. Theory Rel. Fields 124 (2002), no. 3, pp. 345-380 Published version – PDF File
• 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 – PDF File
• Coupling stochastic PDEs
  XIVth International Congress on Mathematical Physics (2005), pp. 281-289
  PDF File
• Amplitude Equations for SPDEs: Approximate Centre Manifolds and Invariant Measures
  Written in collaboration with D. Blömker.
  Proceedings of the IMA, (2004)
  PDF File
• 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 – PDF File
• 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 – PDF File
• 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 – PDF File
• 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 – PDF File
• 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 – PDF File
• 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 – PDF File
• 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 – PDF File
• 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 – PDF File
• 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

  PDF File

• 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 – PDF File
• 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
  PDF File
• 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 – PDF File
• 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)
  PDF File
• 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 – PDF File
• Hypoellipticity in Infinite Dimensions
  Proceedings of ISAAC 09 (2009)
  PDF File
• Singular perturbations to semilinear stochastic heat equations
  Probab. Theory Rel. Fields 152 (2012), no. 1-2, pp. 265-297 Published version – PDF File
• Approximations to the Stochastic Burgers equation
  Written in collaboration with J. Voß.
  Journ. Nonlin. Sci. 12 (2011), no 6, pp. 897-920 Published version – PDF File
• Rough Stochastic PDEs
  Commun. Pure Appl. Math.
  64 (2011), no 11, pp. 1547-1585 Published version – PDF File
• Stochastic PDEs with multiscale structure
  Written in collaboration with D. Kelly.
  Electr. Journ. Probab. 17 (2012), no. 52, pp. 1-38 Published version – PDF File
• 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 – PDF File
• 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 – PDF File
• Solving the KPZ equation
  Annals of Maths 178 (2013), no. 2, pp. 559-664 Published version – PDF File
• 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 – PDF File
• 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 – PDF File
• 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 – PDF File
• A theory of regularity structures
  Invent. Math. 198 (2014), no. 2, pp. 269-504 Published version – PDF File
• Introduction to Regularity Structures
  Braz. Jour. Prob. Stat. 29 (2015), no. 2, pp. 175-210
  Published version – PDF File
• Singular stochastic PDEs
  Proceedings of the ICM (2014)
  PDF File
• 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 – PDF File
• 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 – PDF File
• The dynamical sine-Gordon model
  Written in collaboration with H. Shen.
  Comm. Math. Phys. 341 (2016), no. 3, pp. 933-989
  Published version – PDF File
• 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 – PDF File
• 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 – PDF File
• Multiplicative stochastic heat equations on the whole space
  Written in collaboration with C. Labbé.
  Preprint (2015)
  PDF File
• A central limit theorem for the KPZ equation
  Written in collaboration with H. Shen.
  Preprint (2015)
  PDF File
• Discretisations of rough stochastic PDEs
  Written in collaboration with K. Matetski.
  Preprint (2015)
  PDF File
• A class of growth models rescaling to KPZ
  Written in collaboration with J. Quastel.
  Preprint (2015)
  PDF File
• Large scale behaviour of 3D phase coexistence models
  Written in collaboration with W. Xu.
  Preprint (2016)
  PDF File
• The motion of a random string
  Preprint (2016)
  PDF File
• The reconstruction theorem in Besov spaces
  Written in collaboration with C. Labbé.
  Preprint (2016)
  PDF File
• The strong Feller property for singular stochastic PDEs
  Written in collaboration with J. Mattingly.
  Preprint (2016)
  PDF File