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
          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.


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