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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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A spatial version of the Itô-Stratonovich correction
Written in collaboration with J. Maas.
Ann. Probab. ?? (201?), no ?, pp. ???-??? Published version
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Rough Burgers-like equations with multiplicative noise
Written in collaboration with H. Weber.
Probab. Theory Rel. Fields ??? (201?), no. ?, pp. ???-??? Published version
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Solving the KPZ equation
Preprint (2011)
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Triviality of the 2D stochastic Allen-Cahn equation
Written in collaboration with H. Weber and M. Ryser.
Preprint (2012)
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Stochastic PDEs with multiscale structure
Written in collaboration with D. Kelly.
Preprint (2012)
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Approximating rough stochastic PDEs
Written in collaboration with Jan Maas and H. Weber.
Preprint (2012)
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