Preprints

Volterra equations driven by rough signals.
With F. Harang. 
Relativistic stable processes in quasiballistic heat conduction in thin film semiconductors.
With P. Chakraborty, A. Shakouri, B. Vermeesch. 
Precise local estimates for hypoelliptic differential equations driven by fractional Brownian motions
With X. Geng, C. Ouyang. 
On the anticipative nonlinear filtering problem and its stability.
With G. Lin, Y. Liu. 
Controlled viscosity solutions of fully nonlinear rough PDEs.
With M. Gubinelli, I. Torrecilla.
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Published

Quenched asymptotics for a 1d stochastic heat equation driven by a rough spatial noise.
Stochastic Process. Appl. 130 (2020), no. 11, 6689–6732.
With P. Chakraborty, B. Gao. X. Chen. 
Discrete rough paths and limit theorems.
Ann. Inst. Henri Poincaré Probab. Stat. 56 (2020), no. 3, 1730–1774.
With Y. Liu. 
Density bounds for solutions to differential equations driven by Gaussian rough paths.
J. Theoret. Probab. 33 (2020), no. 2, 611648.
With B. Gess, C. Ouyang. 
A general drift estimation procedure for stochastic differential equations with additive fractional noise.
Electron. J. Stat. 14 (2020), no. 1, 10751136.
With F. Panloup, M. Varvenne.

On the necessary and sufficient conditions to solve a heat equation with general additive Gaussian noise.
Acta Math. Sci. Ser. B 39 (2019), no. 3, 669690.
With Y. Hu, Y. Liu. 
Onedimensional reflected rough differential equations.
Stochastic Process. Appl. 129 (2019), no. 9, 32613281.
With A. Deya, M. Hofmanová, M. Gubinelli. 
LAN property for stochastic differential equations with additive fractional noise and continuous time observation.
Stochastic Process. Appl. 129 (2019), no. 8, 28802902.
With Y. Liu, E. Nualart. 
A priori estimates for rough PDEs with application to rough conservation laws.
J. Funct. Anal. 276 (2019), no. 12, 35773645.
With A. Deya, M. Hofmanová, M. Gubinelli. 
Rough differential equations with power type nonlinearities.
Stochastic Process. Appl. 129 (2019), no. 5, 15331555.
With P. Chakraborty. 
Firstorder Euler scheme for SDEs driven by fractional Brownian motions: the rough case.
Ann. Appl. Probab. 29 (2019), no. 2, 758826.
With Y. Liu. 
Rate of convergence to equilibrium of fractional driven stochastic differential equations with rough multiplicative noise.
Ann. Probab. 47 (2019), no. 1, 464518.
With A. Deya, F. Panloup. 
Parabolic Anderson model with rough dependence in space.
Computation and combinatorics in dynamics, stochastics and control, 477498, Abel Symp., 13, 2018.
With Y. Hu, J. Huang, K. Lê, D. Nualart. 
Stochastic heat equation with rough dependence in space.
Ann. Probab. 45 (2017), no. 6B, 45614616.
With Y. Hu, J. Huang, K. Lê, D. Nualart. 
On a priori estimates for rough PDEs.
Stochastic analysis and related topics, 117138, Progr. Probab., 72, Birkhäuser, 2017.
With Q. Feng. 
Spatial asymptotics for the parabolic Anderson model driven by a Gaussian rough noise.
Electron. J. Probab. 22 (2017), Paper No. 65, 38 pp.
With X. Chen, Y. Hu, D. Nualart. 
Young differential equations with power type nonlinearities.
Stochastic Process. Appl. 127 (2017), no. 9, 30423067.
With J. León, D. Nualart. 
On probability laws of solutions to differential systems driven by a fractional Brownian motion.
Ann. Probab. 44 (2016), no. 4, 25542590.
With F. Baudoin, E. Nualart, C. Ouyang.

Gaussian type lower bounds for the density of solutions of SDEs driven by fractional Brownian motions.
Ann. Probab. 44 (2016), no. 1, 399443.
With M. Besalú, A. KohatsuHiga.

Monte Carlo methods for light propagation in biological tissues.
Math. Biosci. 269 (2015), 4860.
With C. Lacaux, T. Obara, M. Thomassin, L. Vinckenbosch.

Density convergence in the BreuerMajor theorem for Gaussian stationary sequences.
Bernoulli 21 (2015), no. 4, 23362350.
With Y. Hu, D. Nualart, F. Xu.

Stochastic heat equations with general multiplicative Gaussian noises: Hölder continuity and intermittency.
Electron. J. Probab. 20 (2015), no. 55, 50 pp.
With Y. Hu, J. Huang, D. Nualart.

On ${\scriptsize L^{2}}$ modulus of continuity of Brownian local times and Riesz potentials.
Ann. Probab. 43 (2015), no. 3, 14931534.
With A. Deya, D. Nualart.

Skorohod and Stratonovich integration in the plane.
Electron. J. Probab. 20 (2015), no. 39, 39 pp.
With Khalil Chouk.

Smoothness of the density for solutions to Gaussian rough differential equations.
Ann. Probab. 43 (2015), no. 1, 188239.
With T. Cass, M. Hairer, C. Litterer.

Convergence and performance of the peeling wavelet denoising algorithm.
Metrika 77 (2014), no. 4, 509537.
With A. Gueudin, C. Lacaux, R. Ranta.

A least squaretype procedure for parameter estimation in stochastic differential equations with additive fractional noise.
Stat. Inference Stoch. Process. 17 (2014), no. 1, 99120.
With A. Neuenkirch.

Upper bounds for the density of solutions to stochastic differential equations driven by fractional Brownian motions.
Ann. Inst. Henri Poincaré Probab. Stat. 50 (2014), no. 1, 111135.
With F. Baudoin, C. Ouyang.

Spectral Features Selection and Classification for Bimodal Optical Spectroscopy Applied to Bladder Cancer in vivo Diagnosis.
IEEE Trans. on Biomedical Engin. 61 (2014), no. 1, 207216.
With E. Pery, W. Blondel, M. Ghribi, A. Leroux, F. Guillemin. 
Approximation of stationary solutions to SDEs driven by multiplicative fractional noise.
Stochastic Process. Appl. 124 (2014), no. 3, 11971225.
With S. Cohen, F. Panloup.

Model selection for the $\ell^{2}$SVM by following the regularization path.
Transactions on Computational Intelligence 13 (2014), 83112.
With R. Bonidal, Y. Guermeur.

Malliavin calculus for fractional heat equation.
Malliavin calculus and stochastic analysis, 361384, Springer Proc. Math. Stat. 34 , Springer, 2013.
With A. Deya.

Smooth density for some nilpotent rough differential equations.
J. Theoret. Probab. 26 (2013), no. 3, 722749.
With Y. Hu.

On Stratonovich and Skorohod stochastic calculus for Gaussian processes.
Ann. Probab. 41 (2013), no. 3, 16561693.
With M. Jolis, Y. Hu.

On inference for fractional differential equations.
Stat. Inference Stoch. Process. 16 (2013), no. 1, 2961.
With A. Chronopoulou.

An analysis of a stochastic model for bacteriophage systems.
Math. Biosci. 241 (2013), no. 1, 99108.
With D. Bascompte, X. Bardina, C. Rovira.

Malliavin Calculus for Fractional Delay Equations.
J. Theoret. Probab. 25 (2012), no.3, 854889.
With J. León.

Nonlinear rough heat equations.
Probab. Theory Related Fields 153 (2012), no. 12, 97147.
With A. Deya, M. Gubinelli.

A Milsteintype scheme without Lévy area terms for SDEs driven by fractional Brownian motion.
Ann. Inst. Henri Poincaré Probab. Stat. 48 (2012), no. 2, 518550.
With A. Deya, A. Neuenkirch.

Pathwise definition of secondorder SDEs.
Stochastic Process. Appl. 122 (2012), no. 2, 466497.
With L. Quer.

Rough Volterra equations 2: Convolutional generalized integrals.
Stochastic Process. Appl. 121 (2011), no. 8, 18641899.
With A. Deya.

The rough path associated to the multidimensional analytic fBm with any Hurst parameter.
Collect. Math. 62 (2011), no. 2, 197223.
With J. Unterberger.

A construction of the rough path above fractional Brownian motion using Volterra's representation.
Ann. Probab. 39 (2011), no. 3, 10611096.
With D. Nualart.

A model of continuous time polymer on the lattice.
Commun. Stoch. Anal. 5 (2011), no. 1, 103120.
With D. Márquez, C. Rovira.

Stochastic heat and wave equations on a Lie group.
Stoch. Anal. Appl. 28 (2010), no. 4, 662695.
With S. Peszat.

Weak approximation of fractional SDEs: the Donsker setting.
Electron. Commun. Probab. 15 (2010), 314329.
With X. Bardina, C. Rovira.

Rough evolution equations.
Ann. Probab. 38 (2010), no. 1, 175.
With M. Gubinelli.

Discretizing the fractional Lévy area.
Stoch. Process. Appl. 120 (2010), no. 2, 223254.
With A. Neuenkirch, J. Unterberger.

Weak approximation of a fractional SDE.
Stoch. Process. Appl. 120 (2010), no. 1, 3965.
With X. Bardina, I. Nourdin, C. Rovira.

Rough Volterra equations 1: the algebraic integration setting.
Stoch. Dyn. 9 (2009), no. 3, 437477.
With A. Deya.

Trees and asymptotic expansions for fractional stochastic
differential equations. Ann. Inst. Poincaré 45 (2009), no. 1, 157174.
With A. Neuenkirch, I. Nourdin, A. Rössler.

Delay equations driven by rough paths.
Elec. J. of Probab. 13 (2008), no. 67, 20312068.
With A. Neuenkirch, I. Nourdin.

Itô's formula for linear fractional PDEs.
Stoch. Stoch. Reports 80 (2008), 427450.
With J. León.

On homogeneous pinning models and penalizations.
Stoch. Dyn. 8 (2008), 383396.
With M. Gradinaru.

Sharp asymptotics for the partition function of some continuoustime directed polymers.
Potential Anal. 29 (2008), 139166.
With A. Cadel, F. Viens.

Superdiffusivity for a Brownian polymer in a continuous Gaussian environment.
Ann. Probab. 36 (2008), 16421675.
With S. de Carvalho, F. Viens.

A diluted version of the perceptron model.
Stoch. Process. Appl. 117 (2007), 17561785.
With D. Márquez, C. Rovira.

The 1d stochastic wave equation driven by a fractional Brownian motion.
Stoch. Process. Appl. 117 (2007), 14481472.
With Ll. Quer.

On the multiple overlap function of the SK model.
Publ. Mat. 51 (2007), 163199.
With S. Bezerra.

A central limit theorem for a localized version of the SK model.
Potential Anal. 25 (2006), 307326.
With S. Bezerra.

Young integrals and SPDEs.
Potential Anal. 19 (2006), 234253.
With M. Gubinelli, A. Lejay.

Asymptotic behavior of the magnetization for the perceptron model.
Ann. Inst. Poincaré 42 (2006), 327342.
With D. Márquez, C. Rovira.

Relating the almostsure Lyapunov exponent of a parabolic SPDE and its coefficients' spatial regularity.
Potential Anal. 22 (2005), no. 2, 101125.
With C. Tudor, F. Viens.

Itô and Tanaka type formulae for the stochastic heat equation.
J. Funct. Anal. 228 (2005), 114143.
With M. Gradinaru, I. Nourdin.

On the Brownian directed polymer in a Gaussian random environment.
J. Funct. Anal. 222 (2005), 178201.
With C. Rovira.

On the stochastic calculus method for spin systems.
Ann. Probab. 33 (2005), 561581.

A BerryEsseen theorem for FeynmanKac and interacting particle models.
Ann. Appl. Probab. 15 (2005), 941962.
With P. Del Moral.

Sharp Gaussian regularity on the circle, and applications to the fractional stochastic heat equation.
J. Funct. Anal. 217 (2004), 280313.
With C. Tudor, F. Viens.

Higher order expansions for the overlap of the SK model.
Progress in Probability 58 (2004), 2143.
With X. Bardina, D. Márquez, C. Rovira.

The pspins interaction model with external field.
Potential Anal. 21 (2004), 311362.
With X. Bardina, D. Márquez, C. Rovira.
 Convergence of a branching particle system to the solution of a parabolic SPDE on the circle.
Random Operators Stoch. Equ. 12 (2004), 129144.
With F. Viens.
 Stochastic evolution equations with fractional Brownian motion.
Probab. Theory Related Fields 127 (2003), 186204.
With C. Tudor, F. Viens.
 OnsagerMachlup functional for stochastic evolution equations in a class of norms.
Stoch. Anal. Appl. 21 (2003), 12311253.
With X. Bardina, C. Rovira.
 On exponential moments for functionals defined on the loop group.
Stoch. Anal. Appl. 21 (2003), 13331352.
With D. Márquez.
 Probabilistic models for vortex filaments based on fractional Brownian motion.
Ann. Probab. 31 (2003), 18621899.
With D. Nualart, C. Rovira.
 Quenched large deviation principle for the overlap of a pspins system.
J. Stat. Phys. 110 (2003), 5172.
 Onsager Machlup functional for stochastic evolution equations.
Ann. Inst. Poincaré 39 (2003), 5983.
With X. Bardina, C. Rovira.
 Almost sure exponential behaviour for a parabolic SPDE on a manifold.
Stoch. Process. Appl. 100 (2002), 5374.
With F. Viens.
 Asymptotic evaluation of the Poisson measure for tubes around jump curves.
Appl. Matematicae 29 (2002), 145156.
With X. Bardina, C. Rovira.
 Regularity conditions for parabolic SPDEs on Lie groups.
Progress in Probability 52 (2002), 269291.
With F. Viens.
 On forward stochastic integrals over the loop space.
Stoch. Anal. Appl. 20 (2002), 221241.
 Probabilistic models for vortex filaments based on fractional Brownian motion.
Revista de la Real Academia de Ciencias Serie A Matemáticas 95 (2001), 213218.
With C. Rovira, D. Nualart.
 Sharp Laplace asymptotics for an hyperbolic SPDE.
Stochastic analysis and related topics VII: the Kusadasi workshop (2001).
With C. Rovira.
 Sharp large deviation estimates for the stochastic heat equation.
Potential Anal. 14 (2001), 409435.
With C. Rovira.
 Sharp large deviation estimates for a certain class of sets on the Wiener space.
Bull. Sc. Math. 124 (2000), 525555.
With C. Rovira.
 SPDEs with pseudodifferential generators: the existence of a density.
Appl. Matematicae 27 (2000), 287308.
 Sharp Laplace asymptotics for a parabolic SPDE.
Stoch. Stoch. Reports 69 (2000), 1130.
With C. Rovira.
 On spacetime regularity for the stochastic heat equation on Lie groups.
J. Funct. Anal. 169 (1999), 559603.
With F. Viens.
 On nondegenerate two parameter martingales.
Bull. Sc. Math. 122 (1998), 317337.
With D. Nualart.
 Stochastic parabolic equations with anticipative initial condition.
Stoch. Stoch. Reports 62 (1997), 120.
 Quasilinear stochastic hyperbolic differential equations with nondecreasing coefficient.
Potential Anal. 7 (1997), 661680.
With D. Nualart.
 Quasilinear stochastic elliptic differential equations with reflexion: the existence of a density.
Benoulli 5 (1997), 223242.
 Diffusion approximation for elliptic stochastic differental equations.
Stochastic analysis and related topics V: the Silivri workshop (1996), 255269.
 Quasilinear stochastic elliptic differential equations with reflexion.
Stoch. Process. Appl. 57 (1995), 7382.
With D. Nualart.
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