Publications since 2000
 

2000

  1. S. Moret, D. Nualart: Quadratic covariation and Itô's formula for smooth nondegenerate martingales. Journal of   Theoretical Probability 13, 193-224, 2000.
  2. E. Alòs, O. Mazet, D. Nualart: Stochastic calculus with respect to fractional Brownian motion with Hurst parameter less that 1/2. Stochastic Processes and Their Applications 86, 121-139, 2000.
  3. J. León, D. Nualart and R. Pettersson: The stochastic Burgers equation: finite moments and smoothness of the density. Infinite Dimensional Análisis, Quantum Probability and Related Topics 3, 363-385, 2000.
  4. J. León, D. Nualart: Anticipating integral equations. Potential Analysis 13, 249-268, 2000.
  5. D. Nualart, C. Rovira: Large deviations for stochastic Volterra equations. Bernoulli6, 339-355, 2000.\
  6. D. Nualart, F.  Viens: Evolution equation of a stochastic semigroup with white-noise drift. Annals of Probability. 28, 36-73, 2000.
  7. E. Alòs, D. Nualart, F. Viens: Stochastic heat equation with white-noise drift. Annales  Institut Henri Poincaré 36, 181-218, 2000.
  8. D. Nualart, W. Schoutens: Chaotic and predictable representations for Lévy processes. Stochastic Processes and Their Applications 90, 109-122, 2000.
         2001

  1. D. Nualart and Wim Schoutens: BSDE's and Feynman-Kac formula for Lévy processes with applications in finance. Bernoulli 7, 761-776, 2001.
  2. D. Nualart, C. Rovira and S. Tindel: Probabilistic models for vortex filaments based on fractional Brownian motion. Rev. R. Acad. Cien. Serie A. Mat. 95, 213-218, 2001.
  3. S. Moret, D. Nualart: : Generalization of Itô's formula for smooth nondegenerate martingales. Stochastic Processes and Their Applications 91, 115-149, 2001.
  4. E. Alòs, O. Mazet and D. Nualart: Stochastic calculus with respect to Gaussian processes. Annals of Probab. 29, 766-801, 2001.
  5. S. Moret and D. Nualart: Exponential inequalities for two-parameter martingales. Statistics and Probability Letters 54, 13-19, 2001.
  6. E. Alòs, J. A. León and D. Nualart:  Stratonovich stochastic calculus for fractional Brownian motion with Hurst parameter lesser that 1/2. Taiwanese Journal of Mathematics 5, 609-632, 2001.
  7. L. Coutin, D. Nualart and C. Tudor: Tanaka formula for the fractional Brownian motion. Stochastic Processes and Their Applications 94, 301-315, 2001.
  8. D. Nualart and A. Rascanu: Differential equations driven by fractional Brownian motion. Collectanea Mathematica 53, 55-81, 2001.
       2002
  1. K. Burdzy and D. Nualart: Brownian motion reflected on Brownian motion. Probab. Theory Related Fields. 122, 471-493, 2002.
  2. N. Lanjri Zaidi and  D. Nualart: Backward stochastic differential equations in the plane. Potential Analysis 16, 373-386, 2002.
  3. S. Moret and D. Nualart: Onsager-Machlup functional for the fractional Brownian motion. Probab. Theory Rel. Fields 124, 227-260, 2002. 
  4. D. Nualart and Y. Ouknine: Regularization of differential equations by fractional noise. Stochastic Proc. Appl. 102, 103-116, 2002.
         2003
  1. J. A. León, R.Navarro and D. Nualart: An anticipating calculus approach to the utility maximization of an insader. Mathematical Finance 13, 171-185, 2003. 
  2. M. Erraoui, D. Nualart and Y. Ouknine: Hyperbolic stochastic partial diferential equations with additive fractional Brownian sheet. Stochastic Dynamics 3, 121-139, 2003.
  3. D. Nualart and Y. Ouknine: Besov regularity of stochastic integrals with respect to the fractional Brownian motion with parameter  H>1/2. Journal of Theoretical Probability  16, 451-470, 2003.  
  4. D. Nualart, C. Rovira and S. Tindel: Probabilistic models for vortex filaments based on fractional Brownian motion. Annals of Probability 31, 1862-1899, 2003. 
  5. E. Alòs and D. Nualart: Stochastic integration with respect to the fractional Brownian motion. Stochastics and Stochastics Reports 75, 129-152, 2003. 
  6. B. Maslowski and D. Nualart: Evolution equations driven by a  fractional Brownian motion. Journal of Functional Analysis 202, 277-305, 2003. 
  7. F. Baudoin and D. Nualart: Equivalence of Volterra processes. Stochastic Processes and their Applications 107, 327-350, 2003.  
  8. N. Lanjri Zaïdi and D. Nualart: Smoothness of the law of the supremum of the fractional Brownian motion. Electronic Comm. in Probability 8, 1-10, 2003. 
  9. D. Nualart and Y. Ouknine:  Stochastic differential equations with additive fractional noise and locally unbounded drift. Progress in Probability 56, 353-365, 2003
  10. D. Nualart: Stochastic calculus with respect to the fractional Brownian motion and applications. Contemporary Mathematics 336, 3-39, 2003.  
          2004
  1.  J. M. Corcuera, P. Imkeller, A. Kohatsu-Higa and D. Nualart: Additional utility of insiders with imperfect dynamical information. Finance Stochast. 8,   437-450, 2004.
  2. D. Nualart and Y. Ouknine:  Regularization of quasilinear heat equation equations by a fractional noise. Stochastics and Dynamics 4, 201-221, 2004.
  3. Yu. Mishura and D. Nualart: Weak solutions for stochastic differential equations with additive fractional noise.  Statistics and Probability Letteres 70, 253-261, 2004.
          2005

  1. G. Peccati and D. Nualart: Central limit theorems for sequences of multiple stochastic integrals. Annals of Probability 33, 177-193, 2005.
  2. Y. Hu and D. Nualart: Some processes associated with fractional Brownian motion. J. Theoret. Probab. 18, 377-307, 2005.
  3. Y. Hu and D. Nualart: Renormalized self-intersection local time for fractinal Brownian motion. Ann. Probab. 33, 948-983, 2005.
  4. J. Guerra and D. Nualart: The 1/H-variation of the divergence integral with respect to the fractional Brownian motion for H>1/2 and fractional Bessel processes. Stochastic Proc. Appl. 115, 91-115, 2005.
  5. P. Cheridito and D. Nualart: Stochastic integral of divergence type with respect to fractional Brownian motion with Hurst parameter H in (0,1/2). Ann. I. H. Poincare 41, 10491081, 2005.
  6. J. M. Corcuera, D. Nualart and  W. Schoutens: Completion of a Lévy Market by Power-Jump Assets. Finance Stochast. 9, 109-127, 2005.

          2006
  1. F. Baudoin and D. Nualart: Notes on the two-dimensional fractional Brownian motion. Ann. Probab. 34, 159-180, 2006.
  2. J. M. Corcuera, J. Guerra, D. Nualart and  W. Schoutens: Optimal investment in a Lévy Market. Appl. Math. Optim. 53, 279-309, 2006.
  3. J. M. Corcuera, D. Nualart and J. H. C. Woerner: Power variation of some integral long-memory processes. Bernoulli  12, 713-735, 2006.
  4. D. Nualart and M. Taqqu: Wick-Ito formula for Gaussian processes Stoch. Anal. Appl. 24, 599-614, 2006.
  5. D. Nualart and P. Vuillermot:  Stabilization phenomenon for a class of stochastic partial differential equations. Stochastic partial differential equations and applications---VII, 215-227, Lect. Notes Pure Appl. Math., 245, Chapman & Hall/CRC, Boca Raton, FL, 2006.
  6. D. Nualart and P. Vuillermot: Variational solutions for partial differential equations driven by fractional noise. Journal of Functional Analysis. 232, 390-454, 2006.
  7. D. Nualart: Stochastic calculus with respect to fractional Brownian motion. Ann  Fac.  Sci.    Toulouse 15,  63-78, 2006.
  8. J. Leon and D. Nualart: Clark-Ocone formula for fractional Brownian motion with Hurst parameter less than 1/2. Journal of Stochastic Analysis and Applications 24, 427-449, 2006.
          2007
  1. D. Nualart, S. Ortiz-Latorre: Intersection local time for two independent fractional Brownian motions. J. Theor. Probability 20, 759-757, 2007.
  2. D. Nualart, Ll. Quer-Sardanyons: Existrence and smoothness of the density for spatially homogeneous SPDEs. Potential Anal. 27, 281-299, 2007.
  3. Y. Hu and D. Nualart: Regularity of renormalized self-intersection local time for fractional Brownian motion. Communications in Information and Systems 7, 21-30, 2007.
  4. J. M. Corcuera, D. Nualart and  J. H. C. Woerner: A functional central limit theorem for the realized power variation of integrated stable process. Journal of Stochastic Analysis and Applications 25, 169-186, 2007.
  5. L. Decreusefond and D. Nualart: Flow properties of differential equations driven by fractional Brownian motion.  In:  Stochastic Differential Equations - Theory and Applications, 249--262, eds: Peter Baxendale and Sergey Lototsky. Interdiscip. Math.Sci., 2, World Sci. Publ., Hackensack, NJ, 2007. Arxiv file.
  6. Y. Hu and D. Nualart:  Differential equations driven by Holder continuous functions of order greater than 1/2.  In:  Stochastic Annalysis and Applications, 399-413,  Abel Symp., 2, Springer, Berlin, 2007. Arxiv file
        2008
  1. L. Decreusefond and D. Nualart: Hitting times for Gaussian processes. Annals of Probability 36, 319-330, 2008.
  2. D. Nualart, S. Ortiz-Latorre: Central limit theorem for multiple stochastic integrals and Malliavin calculus. Stochastic Processes and Their Applications 118, 614-628, 2008.
  3. D. Nualart and M. Taqqu: Wick-It\^o formula for regular processes and applications to the Black and Scholes formula. Stochastics 80, 477-487, 2008.
  4. J. Guerra and D. Nualart: Stochastic differential equations driven by fractional Brownian motion and a standard Brownian motion. Journal of Stochastic Analysis and Applications 26, 1053-1075, 2008. Arxiv file.
  5. Y. Hu, D. Nualart and X. Song: A singular stochastic differential equation driven by fractional Brownian motion. Statistics and Probability Letters 75, 2075-2085, 2008. Arxiv file.
  6. J. Feng and D. Nualart: Stochastic scalar conservation laws. Journal of Functional Analysis 55, 313-371, 2008
  7. D. Nualart and S. Ortiz-Latorre: It\^o-Stratonovich formula for Gaussian processes: a Riemann sums approach. Stochastic Processes and their Applications 118, 1803-1819, 2008.
  8. C. Mueller and D. Nualart: Regularity of the density for the stochastic heat equation.   Electronic Journal of Probability 74, 2248-2258, 2008. Arxiv file.
  9. Y. Hu, D. Nualart and J. Song: Integral representation of renormalized self-intersection local times. Journal of Functional Analysis 255, 2507-2532, 2008. Arxiv file.

2009

  1. Y. Hu and D. Nualart: Stochastic heat equation driven by fractional noise and local times. Probability Theory and Related Fields 143, 285-328, 2009. Arxiv file.
  2. D. Nualart and B. Saussereau: Malliavin calculus for stochastic differential equations driven by a fractional Brownian. motion. Stochastic Processes and their Applications 119, 391-409, 2009.
  3. Y. Hu and D. Nualart: Rough path analysis via fractional calculus. Transactions of the American Mathematical Society 361, 2689-2718, 2009. Arxiv file
  4. P. Lei and D. Nualart: A decomposition of the bifractional Brownian motion and some applications. Statistics and Probability Letters 79, 619-624, 2009. Arxiv file.
  5. Y. Hu and D. Nualart: Stochastic integral representation of the L^2 modulus of continuity of Brownian local time and a central limit theorem. Electronic Communications in Probability 14, 529-539, 2009 Arxiv file.
  6. Y. Hu, D. Nualart, J. Song: Fractional martingales and characterization of the fractional Brownian motion. Annals of Probability 37, 2404-2430, 2009. Arxiv file.
  7. D. Nualart and Ll. Quer-Sardanyons: Gaussian estimates for solutions to quasi-linear stochastic partial differential equations. Stochastic Processes and Applications 119, 3914-3938, 2009. Arxiv file.
  8. D. Nualart and T. Duncan: Existence of strong solutions and uniqueness in law for stochastic differential equations driven by fractional Brownian motion.  Stochastic and Dynamics 9, 423-435, 2009.
  9. J. M. Corcuera, D. Nualart and J. H. C. Woerner: Convergence of certain functionals of integral fractional processes. Journal of Theoretical Probability 23, 856-971, 2009.

2010

  1. S. Darses, I. Nourdin and D. Nualart: Limit theorems for nonlinear functionals of Volterra processes via white noise analysis. Bernoulli 16(4), 1262-1293, 2010 Arxiv file.
  2. I. Nourdin, D. Nualart, C. Tudor: Central and non-central limit theorems for weighted power variations of fractional Brownian Motion. Annals de l'Institut Henri Poincare 46, 1055-1079, 2010.  Arxiv file.
  3. Y. Hu and D. Nualart: Central limit theorem for the third moment in space of the Brownian local time increments. Electronic Communications in Probability 15, 396-410, 2010. File.
  4. I. Nourdin, D. Nualart: Central limit theorems for multiple Skorohod integrals. Journal of Theoretical Probability 23, 39-64, 2010. Arxiv file.
  5. Y. Hu and D. Nualart: Parameter estimation for fractional Ornstein-Uhlenbeck processes. Statistics and Probability Letters 80, 1030-1038, 2010. Arxiv file.
  6. K. Es-Sebaiy, D. Nualart, Y. Ouknine, C. Tudor: Occupation densities for certain processes related to fractional Brownian motion. Stochastics 82, 133-147, 2010 Arxiv file.

2011

  1. Y. Hu, D. Nualart and J. Song: Feynman-Kac formula for heat equation driven by fractional white noise. Annals of Probability 39, 291-326, 2011. Arxiv file.
  2. D. Nualart and L. Quer-Sardanyons: Optimal Gaussian density estimates for a class of stochastic equations with additive noise. Infinite Dimensional Analysis, Quantum Probability and Related Topics 14, 25-34, 2011. Arxiv file.
  3. D. Nualart and S. Tindel: A construction of the rough path above fractional Brownian motion using Volterra's representation. Annals of Probability 39, 1061-1096, 2011.Arxiv file.
  4. Y. Hu, D. Nualart and X. Song: Malliavin calculus for backward stochastic differential equations and application to numerical solutions. Annals of Applied Probability. 21, 2379-2423, 2011.  File.
  5. M. Besalú and D. Nualart: Estimates for the solution to stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H in(1/3,1/2). Stochastics and Dynamics 11, 243-263, 2011.
  6. D. Nualart and S. Ortiz-Latorre:  Multidimensional Wick-Ito formula for Gaussian processes. In: Stochastic Analysis, Stochastic Systems and Applications to Finance. Ed: A. Tsoi, D. Nualart and G. Yin, World Scientific 2011, 3-26.
  7. H. Hu, D. Nualart, X. Weilin and Z. Weiguo: Exact maximum likelihood estimator for drift fractional Brownian motion at discrete observations. Acta Mathematica Scientia 31B, 1851-1859, 2011.

       2012
  1. Y. Hu, F. Lu and D. Nualart: Feynman-Kac formula for the heat equation driven by fractional noise with Hurst parameter H<1/2. Annals of Probability 40, 1041-1068, 2012. Arxiv file.
  2. D. Harnett and D. Nualart: Weak convergence of the Stratonovich integral with respect to a class of Gaussian processes. Stochastic Processes and Their Applications. 122, 3460-3505, 2012.   Arxiv file.
  3. P. Lei and D. Nualart: Stochastic calculus for Gaussian processes and application to hitting times. Communications in Stochastic Analysis 6, 379-402, 2012.

       2013

  1. Y. Hu, D. Nualart and J. Song: A nonlinear stochastic heat equation: Hölder continuity and smoothness of the density of the solution. Stochastic Process and Their Applications 123, 1083-1103, 2013. Arxiv file.
  2. I. Nourdin, D. Nualart and G. Poly: Absolute continuity and convergence of densities for random vectors on Wiener chaos. Electronic Journal of Probability 18, 1-19, 2013. Arxiv file.
  3. D. Harnett and D. Nualart: Central limit theorem for a Stratonovich integral with Malliavin Calculus. Annals of Probability 41, 2820-2879, 2013. Arxiv file.
  4. D. Nualart and F. Xu: Central limit theorem for an additive functional of the fractional Brownian motion II. Electronic Communications in Probability 18,  no 74, 1-10, 2013. Arxiv file.
  5. Y. Hu, F. Lu and D. Nualart: Hölder continuity of the solution for a class of nonlinear SPDEs arising from one-dimensional superprocesses. Probability Theory and Related Fields  156, 27-49, 2013. Arxiv file.
  6. D. Nualart and J. Swanson: Joint convergence along different subsequences of the signed cubic variation of fractional Brownian motion II. Electronic Communications in Probability 18,  no 81, 1-10, 2013. Arxiv file.
  7. Y. Hu, F. Lu and D. Nualart:  Non-degeneracy of some Sobolev pseudo-norms of fractional Brownian motion. Electronic Communications in Probability 18,  no 84, 1-10, 2013.  Arxiv file.

      2014

  1. Y. Hu, D. Nualart and F. Xu: Central limit theorem for an additive functional of the fractional Brownian motion. Annals of Probability  42,  168-203, 2014. Arxiv file.
  2. Y. Hu, F. Lu and D. Nualart: Convergence of densities for some functionals of Gaussian processes. J. Funct. Anal. 266, 814-875, 2014. Arxiv file.
  3. Y. Hu, D. Nualart and J. Song: The 4/3-variation of the derivative of the self-intersection Brownian local time and related processes. Journal of Theoretical Probability.  27, 789-825, 2014.   Arxiv file.
  4. C. Burdzy, D. Nualart and J. Swanson: Joint convergence along different subsequences of the signed cubic variation of fractional Brownian motion. Probability Theory and Related Fields.  159, 237-272, 2014 Arxiv file.
  5. J. Huang, Y. Hu and D. Nualart: On Hölder continuity of the solution of stochastic wave equations. Stochastic Partial Differential Equations: Analysis and Computations. 2, 353-407, 2014.  Arxiv file.
  6. D. Harnett and D. Nualart: Central limit theorem for an iterated integral with respect to fBm with H>1/2. Stochastics 86, 187-202, 2014.  Arxiv file.
  7. D. Nualart and F. Xu: Central limit theorem for functionals of two independent fractional Brownian motions. Stochastic Processes and Their Applications 124, 3782-3806, 2014. Arxiv file.
  8. D. Nualart and V. Pérez-Abreu: On the eigenvalue process of a matrix fractional Brownian motion. Stochastic Processes and Their Applications 124, 4266-4282, 2014. Arxiv file.
  9. D. Nualart and F. Xu: A second order limit law for occupation times of the Cauchy process.  Stochastics 86,  967-974, 2014.  Arxiv file.
  10. J. M. Corcuera, D. Nualart and M. Podolskij: Asymptotics of weighted random sums. Communications in Applied and Industrial Mathematics 6, no. 1, e-486, 2014. Arxiv file.

          2015

  1. A. Deya, D. Nualart, S. Tindel: On L^2 modulus of continuity of Brownian local times and Riesz potentials. Annals of Probability 43, 1493-1534, 2015. Arxiv file.
  2. Y. Hu, J. Huang, D. Nualart and S. Tindel: Stochastic heat equations with general multiplicative Gaussian noises: Hölder continuity and intermittency. Electronic Journal in Probability 20, 1-50, 2015. Arxiv file.
  3. Y. Hu, D. Nualart, S. Tindel and F. Xu: Density convergence in the Breuer-Major theorem for Gaussian stationary sequences. Bernoulli 21 (4), 2336-2350, 2015. Arxiv file.
  4. E. H. Essaky and D. Nualart: On the 1/H-variation of the divergence integral with respect to a fractional Brownian motion with Hurst parameter H<1/2. Stochastic Processes and Their Applications 11, 4117-4141, 2015.  Arxiv file.
  5. Y. Hu, J. Huang, D. Nualart and X. Sun: Smoothness of the joint density for spatially homogeneous SPDEs. Journal of the Mathematical Society of Japan 67, no. 4, 1605-1630, 2015. Arxiv file.
  6. D. Harnett and D. Nualart: On Simpson's rule and fractional Brownian motion with H = 1/10. Journal of Theoretical Probability 28, 1651-1688, 2015.  Arxiv file.

      2016
  1. I. Nourdin, D. Nualart and G. Peccati: Strong asymptotic independence on Wiener chaos. Proceedings of the AMS. 144, 875-886, 2016. Arxiv file.
  2. I. Nourdin, D. Nualart and G. Peccati: Quantitative stable limit theorems on the Wiener space. Annals of Probability 44 no 1, 1-41, 2016 Arxiv file.
  3. Y. Hu, Y. Lui and D. Nualart: Rate of convergence and asymptotic error distribution of Euler approximation schemes for fractional diffusions. Annals of Applied Probability 26 no 2, 1147-1207, 2016. Arxiv file.
  4. Y. Hu, J. Huang and D. Nualart: On the intermittency front of stochastic heat equation driven by colored noises. Electronic Communications in Probabililty 21 no 21, 1-13, 2016. Arxiv file.
  5. I. Nourdin and D. Nualart: Fisher Information and the Fourth Moment Problem. Annals of the Institut Henri Poincaré  52  no 2, 849-867, 2016. Arxiv file.
  6. Y. Hu, Y. Liu and D. Nualart: Taylor schemes for rough differential equations and fractional diffusions. Discrete and Continuous Dynamical Systems Series B 21 no 9, 3115-3162, 2016.     Arxiv file.
  7. I. Nourdin, D. Nualart and R. Zintout: Multivariate central limit theorems for averages of fractional Volterra processes and applications to parameter estimation. Statistical Inference for Stochastic Processes 19 no 2, 219-234, 2016. Arxiv file.

           2017

  1. A. Jaramillo and D. Nualart: Asymptotic properties of the derivative of self-intersection local itme of fractional Brownian motion. Stochastic Processes and Their Applications 217, 669-700, 2017 Arxiv file.
  2. D. Nualart and C. Tudor: The determinant of the iterated Malliavin matrix and the density of a pair of multiple integrals. Annals of Probability 45, no 1, 518-534, 2017 Arxiv file.
  3. Y. Hu, J. Huang, K. Le, D. Nualart and S. Tindel: Stochastic heat equation with rough dependence in space. Annals of Probability. To appear. Arxiv file.
  4. J. Huang, K. Le and D. Nualart: Large time asymptotics for the parabolic Anderson model driven by spatially correlated noise.  Annals of the Institut Henri Poincaré 53, no. 3, 1305-1340, 2017.  Arxiv file.
  5. X. Chen, Y. Hu, D. Nualart and S. Tindel: Spatial asymptotics for the parabolic Anderson model driven by a Gaussian rough noise. Electronic Journal of Probability 22, no.1, 1-38, 2017. Arxiv file.
  6. L. Chen, Y. Hu and D. Nualart: Two-point correlation function and Feynman-Kac formula for the stochastic heat equation. Potential Analysis  45, no 4, 779-797, 2017. Arxiv file.
  7. J. A. León, D. Nualart and S. Tindel: Young differential equations with power type nonlinearities. Stochastic Processes and Their Applications 127, no 9,  3042-3067, 2017. Arxiv file.
  8. D. Harnett and D. Nualart: Central limit theorem for functionals of a generalized self-similar process. Stochastic Processes and Their Applications Arxiv file.
  9. L. Chen, Y. Hu, K. Kalbasi and D. Nualart: Intermittency for the stochastic heat equation driven by a rough time fractional noise. Probability Theory and Related Fields. To appear. Arxiv file.
  10. J. Huang, K. Lê and D. Nualart. Large time asymptotics for the parabolic Anderson model driven by space and time correlated noise. Stochastics and Partial Differential Equations. To appear.  Arxiv file.

     2018
  1.  Y. Hu, D. Nualart and T. Zhang: Large deviations for stochastic heat equation with rough dependence in space. Bernoulli 24(1), 354-385, 2018.







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