!!! IN WORK
BOOKS and MONOGRAPHS
Analysis of variations for self-similar processes, Springer, Probability and Its Applications.
(with I. Florescu) Handbook of Probability, John Wiley and Sons.
SOME PREPRINTS:
(with Junfeng Liu) " Analysis of the density of the solution to a semilinear SPDE with fractional noise", 27 pages, 2015, to appear in Stochastics.
(with J. Clarke Dela Cerda and C. Olivera) " The transport equation and zero quadratic variation processes", 14 pages, 2016, to appear in Discrete and Continuous Dynamical Systems Serie B.
(with Yimin Xiao) "Sample paths of the solution to the fractional-colored stochastic heat equation", 18 pages, 2015, to appear in Stochastics and Dynamics.
(with David Nualart) "The determinant of the iterated Malliavin matrix and the density of a couple of multiple integrals", 17 pages, 2015, to appear in The Annals of Probability.
(with S. Kusuoka) "Characterization of the convergence in total variation and extension of the Fourth Moment Theorem to invariant measures of diffusions", 2015, preprint.
(with Soledad Torres) " The Multifractal Random Walk as pathwise stochastic integral: construction and simulation", 22 pages, 2016.
"Multidimensional Selberg theorem and fluctuations of the zeta zeros via Malliavin calculus", 35 pages, Preprint, 2016.
"Chaos expansion and Selberg's theorem for the Riemann zeta function" , 12 pages, 2016.
PUBLICATIONS :
Note: the attached files are the preprints. For the published version, check the journal.
2016:
(with Junfeng Liu) " Central Limit Theorem for the solution to the heat equation with moving time", 21 pages, 2015, to appear in Infinite Dimensional Analysis and Quantum Probability.
(with Alexis Fauth) "Multifractal Random Walk Driven by a Hermite Process", Handbook of High-Frequency Trading and Modeling in Finance, Wiley, 2016.
2015:
(with Christian Olivera) "The density of the solution to the stochastic transport equation with fractional noise", Journal of Mathematical Analysis and Applications, 431 (1), 2015.
(with Khalifa Es-Sebaiy) "Fractional Ornstein-Uhlenbeck processes mixed with a Gamma distribution", Fractals, 3, 1550032, 10pp.
(with S. Bourguin) "On the law of the solution to a stochastic heat equation with fractional noise in time", Random Operators and Stochastic Equations, 23 (3), 179-186, 2015.
(with Cristiana Tudor) "Parameter estimation in the ARCH model with weighted liquidity", The Bulletin of the Transilvania University, Brasov, 8(57), 99-108, 2015.
2014:
(with S. Torres and F. Viens) "Quadratic variations for the fractional-colored stochastic heat equation", Electronic Journal of Probability, 19 (76), 51 pages, 2014.
(with Jean-Marc Bardet) " Asymptotic behavior of the Whittle estimator for the increments of a Rosenblatt process", Journal of Multivariate Analysis, 131, 1-16, 2014.
(with Mounir Zili) " Covariance measure and stochastic heat equation with fractional noise", Fractional Calculus and Applied Analysis, 17 (3), 807-826.
(with Jorge Clarke De la Cerda) " Wiener integrals with respect to the Hermite field and applications to the wave equation", Collectanea Matematica, 65 (3), 341-356, 2014.
" Chaos expansion and asymptotic behavior of the Pareto distribution", Statistics and Probability Letters, 91, 62-68, 2014.
(with M. Clausel, F. Roueff and M. Taqqu) "Asymptotic behavior of the quadratic variation of the sum of two Hermite processes of consecutive orders", Stochastic Processes and Their Applications, 124 (7), 2517-2541, 2014.
(with M. Clausel, F. Roueff and M. Taqqu) "Wavelet estimation of the long memory parameter for Hermite polynomial of Gaussian processes," ESAIM Probability and Statistics, 18, 42-76, 2014.
(with Cristiana Tudor) "EGARCH model with weighted liquidity", Communications in statistics-Simulation and Computation, 43 (5), 1133-1142, 2014.
"Recent developments on stochastic heat equation with additive fractional-colored noise", Fractional Calculus and Applied Analysis, 17(1), 224-246, 2014.
(with Alexis Fauth) "Multifractal random walks with fractional Brownian motion via Malliavin calculus", IEEE Transactions on Information Theory, 60 (3), 1963-1975, 2014.
(with Franco Flandoli and Peter Imkeller) "2D- stochastic currents over the Wiener sheet", Journal of Theoretical Probability, 27 (2), 552-575, 2014.
(with Jorge Clarke De la Cerda) "Hitting times for the stochastic wave equation with fractional-colored noise", Revista Matematica Iberoamericana, 30 (2), 685-709, 2014.
2013:
The determinant of the Malliavin matrix and the determinant of the covariance matrix for multiple integrals", ALEA, 10 (2), 681-692.
(with Solesne Bourguin) "Malliavin calculus and self normalized sums", Séminaire de Probabilités XLV 323-351, Lecture Notes in Mathematics, 2078.
(with Mariela Sued and Soledad Torres) "Nonparametric regression with non-Gaussian long memory", Communications on Stochastic Analysis, 7(2), 255-273, 2013.
(with M. Tudor) " Gamma mixed Ornstein-Uhlenbeck sheet", Publicationes Mathematiques Debrecen, 82 (3-4), 607-622, 2013.
(with Hanae Ouahhabi) "Additive functionals of the solution to fractional stochastic heat equation" , Journal of Fourier Analysis and Applications, 19 (4), 777-791, 2013.
(with Bohdan Maslowski) "Drift parameter estimation for infinite-dimensional fractional Ornstein-Uhlenbeck process", Bulletin des Sciences Mathématiques, 137 (7), 880-901, 2013.
(with M. Tudor) "Fractional 2D currents", Acta Mathematica Scientia Serie B, 33 (6), 1507-1521, 2013.
(with Makoto Maejima) "On the distribution of the Rosenblatt process", Statistics and Probability Letters, 83 (6), 1490-1495.
(with Laura Ramos Rifo and Soledad Torres) "Comparative estimation for discrete fractional Ornstein-Uhlenbeck process", Stochastic Models, 29 (3), 291-305.
Chaos expansion and regularity of the local time of the solution to the stochastic heat equation with additive fractional -colored noise, Taiwanese Journal of Mathematics, 17 (5), 1765-1777, 2013.
(with M. Tudor) " Spatial variations for the solution to the heat equation with additive time-space white noise, " Revue Roumaine Math. Pures Appl. 58 (4), 453-462, 2013.
(with M. Clausel, F. Roueff and M. Taqqu) "High order chaotic limits for wavelet scalogram under long-range dependence", ALEA, 10 (2), 979-1011, 2013.
2012:
(with Seiichiro Kusuoka) "Stein method for invariant measures of diffusions via Malliavin calculus ", 2012, Stochastic Processes and their Applications, 122 (4), 1627-1651, 2012.
(with Makoto Maejima) "Selfsimilar processes with stationary increments in the second Wiener chaos", 2012, Probability and Mathematical Statistics, 32 (1), 167-186, 2012.
(with Johanna Garzon and Soledad Torres) "A strong convergence to the Rosenblatt process" , 2012, Journal of Mathematical Analysis and Applications, 391 (2), 630-647.
(with Jorge Clarke De la Cerda) "Least square estimator for the parameter of the fractional Ornstein-Uhlenbeck sheet", 2012, J. of the Korean Statistical Society, 41 (3), 341-350, 2012.
"Kernel density estimation, local times and chaos expansion", Special Volume "Stochastic Processes and Probability 2012" , Springer series in mathematics, 2012.
(with Anthony RĂ©veillac and Michael Stauch) "Hermite variations of the fractional Brownian sheet", Stochastics and Dynamics, 12 (3), 21 pages, 2012.
(with Solesne Bourguin) "Asymptotic theory for fractional regression models via Malliavin calculus", Journal of Theoretical Probability, 25 (2), 536-564, 2012.
65. (with Marianne Clausel, Francois Roueff and Murad Taqqu) "Large scale behavior of wavelet coefficients of non-linear subordinated processes with long memory", Applied and Computational Harmonic Analysis, 32 (2), 223-241.
2011:
64. (with Solesne Bourguin) "Cramer's theorem for Gamma random variables", 2011,Electronic Communications in Probability, 16, 365-378
63. (with Ionut Florescu) "Estimation of the long memory parameter in stochastic volatility models by quadratic variations", 2011, Random Operators and Stochastic Equations (special volume), 19(2), 197-216.
62. (with Solesne Bourguin) "Berry-Ess\'een Bounds for Long Memory Moving Averages via Stein's Method and Malliavin Calculus", Stochastic Analysis and Applications, 29(5), 881-905
61. "Kernel density estimation, local times and chaos expansion", 2011, 13 pages, to appear in Stochastic Processes and Probability, Springer Special volume.
60. (with Stefano Bonaccorsi) "Dissipative stochastic evolution equations driven by general Gaussian and non-Gaussian noise", Journal of Dynamics and Differential Equations, 23 (4), 791-816, 2012.
59. "On the structure of Gaussian random variables", 2011, Revue Roumaine de Mathematiques Pures et Appliquees, Tome LVI (1), 69-83.
58. (with Karine Bertin and Soledad Torres) "Drift parameter estimation in fractional diffusions, martingales and random walks", 2011, Statistics and Probability Letters, 81, 243-249.
57. (with Karine Bertin et Soledad Torres) "Maximum likelihood estimators and random walks in long-memory models", Statistics, 45 (4), 361-374, 2011.
2010:
56. (with Jean-Marc Bardet) "A wavelet analysis of the Rosenblatt process: chaos expansion and estimation of the self-similarity parameter", 2010, Stochastic Processes and their Applications, 120, 2331-2367.
55. (with Raluca Balan) "The Stochastic Wave Equation with Fractional Noise: a random field approach", 2010, Stochastic Processes and their Applications, 120, 2468-2494.
54. (with Xavier Bardina and Khalifa Es-Sebaiy) "Approximation of the finite dimensional distributions of multiple fractional integrals", Journal of Mathematical Analysis and Applications, 369(2), 694-711.
53. Asymptotic Cramer's theorem and analysis on Wiener space, Seminaire de Probabilites, Lecture Notes in Mathematics, Vol. 43, 309–325, LNM 2006 (2011).
52. (with Alexandra Chronopulou et Frederi Viens) "Self-similarity parameter estimation and reproduction property for non-Gaussian Hermite processes", Communications on Stochastic Analysis, 5(1), 161-185.
51. (with Franco Flandoli) "Brownian and fractional Brownian stochastic currents via Malliavin calculus", 2009, Journal of Functional Analysis, 258(1), 279-306.
50. (with Ivan Nourdin and David Nualart) "Central and non-central limit theorems for weighted power variations of the fractional Brownian motion", 'Annales de l'Institut Henri Poincaré -Probabilités et Statistiques, 46(4), 1055-1079.
49. (with Khalifa Es-Sebaiy) "Non-central limit theorem for the cubic variation of a class of selfsimilar stochastic processes", 2010, "Theory of Probability and its Applications" , 55(1), 1-23.
48. (with Raluca Balan) "Stochastic Heat Equation with Multiplicative Fractional-Colored Noise", 2009, Journal of Theoretical Probability, 23, 834-870.
2009:
47. (with Alexandra Chronopulou et Frederi Viens) "Variations and Hurst index estimation for a Rosenblatt process using longer filters", 2009, Electronic Journal of Statistics, 3, 1393-1435.
46. "Hsu-Robbins and Spitzer's theorems for the variations of fractional Brownian motion", 2009, Electronic Communications in Probability, 14, 278-289.
45. (with Frederi Viens) "Variations and estimators for selfsimilarity parameters via Malliavin calculus" , 2009, The Annals of Probability, 37(6), 2093-2134.
44. (with Alexandra Chronolopoulou and Frederi Viens) "Application of Malliavin calculus and analysis on Wiener space to long-memory parameter estimation for non-Gaussian processes", 2009, C.R.A.S. Mathematiques, vol. 347 (11-12), pag. 663-666.
43. (with Khalifa Es-Sebaiy, David Nualart et Youssef Ouknine) "Occupation densities for certain processes related to fractional Brownian motion", 2010, Stochastics, 82(1-3), 133-147.
42. (with Frederi Viens) "Variations of the fractional Brownian motion via Malliavin calculus", 2009, Proceedings of the JMASA Conference (Safi, Maroc, juin 2008) to appear in Australian Journal of Mathematical Analysis and Applications.
41. (with Xavier Bardina et Maria Jolis) "On the convergence to the multiple Wiener-It^o integral", 2009, Bulletin des Sciences Mathematiques, vol. 133, pag. 257-271.
40. (with Soledad Torres) "Donsker type theorem for the Rosenblatt process and a binary market model", 2009, Stochastic Analysis and Applications, 27(3), pag. 555-573.
2008:
39. (with Makoto Maejima) "Limits of bifractional noises" , 2008, Communications on Stochastic Analysis, vol. 3, 369-383.
38. (with Raluca Balan) "The stochastic heat equation with a fractional colored noise: existence of the solution", ALEA (Latin American Journal of Probability and Statistics) , 2008, vol. 4, pag. 57-87. ( a partial correction can be found here in the appendix)
37. (with Khalifa Es-Sebaiy) "Levy processes and Skorohod integrals", 2008, Theory of Stochastic Processes, vol. 14 (2), pag. 10-18. Proceedings of the conference "Skorohod space conference", Kyiv, June 2007.
36. "Analysis of the Rosenblatt process", ESAIM-Probability and Statistics, 2008, vol. 12, pag. 230-257.
35.(with Tommi Sottinen) "Parameter estimation for stochastic equations with fractional Brownian motion", Statistical Inference for Stochastic Processes, 2008, vol. 11 (3), pag. 221-236.
2007:
34. (with Ida Kruk and Francesco Russo) " Wiener integrals, Malliavin calculus and covariance measure structure", Journal of Functional Analysis, 2007, vol. 249, pag.92-142.
33. (with Khalifa Es-Sebaiy) "Multidimensional bifractional Brownian motion", Stochastics and Dynamics, 2007, vol. 3, pag. 365-388.
32. (with Makoto Maejima) "Wiener integrals and a Non-Central Limit Theorem for Hermite processes", Stochastic Analysis and Applications, 2007, vol. 25 (5), pag. 1043-1056.
31. (with Yimin Xiao) "Sample Path Properties of the Bifractional Brownian Motion", Bernoulli, 2007, vol. 13(3), pag. 1023-1052.
30. (with Frederi Viens) "Statistical aspects of the fractional stochastic calculus", 2006, The Annals of Statistics, 2007, vol. 25 (5), pag. 1183-1212.
29. (with Giovanni Peccati) "Anticipating integrals and martingales on the Poisson space", Random Operators and Stochastic Equations, 2007.
28. (with Xavier Bardina) "The law of a stochastic integral with two independent fractional Brownian motions", Boletin de la Sociedad Matematica Mexicana, 2007, vol. 13(1).
2006:
27. (with Frederi Viens) "Ito formula for the fractional Brownian sheet using the extended divergence integral, Stochastics, 2006, vol. 78 (6), pag. 443-462.
26. (with M'Hamed Eddahbi, Ramon Lacayo, Josep Lluis Sole et Josep Vives) "Renormalization of the local times for $d$ dimensional fractional Brownian motion with $N$ parameters", 2006, Nagoya Mathematical Journal, 207, vol. 186.
25. (with Ivan Nourdin) "Some linear fractional equations", 2006, , Stochastics, 78(2), pag. 51-65.
24. (with Francesco Russo) "On the bifractional Brownian motion", Stochastic Processes and their Applications, 116(5), pag. 830-856.
23. (with Tommi Sottinen) "On the equivalence of multiparameter Gaussian processes", Journal of Theoretical Probability, 2006, vol. 19(2), pag. 461-485.
22. (with Giovanni Peccati et Michele Thieullen) "Martingale structure for Skorohod integral processes", 2006, The Annals of Probability, 34 (3).
2005:
21. "Ito formula for the infinite-dimensional fractional Brownian motion", 2005, Journal of Mathematics of Kyoto University, 45 (3), pag. 531-546.
20. (with Brahim Boufoussi) "Kramers-Smoluchowski approximation for stochastic equations with fractional Brownian motion", 2005, Revue Roumaine de Math\'ematiques Pures et
Appliqu\'ees, Tome 50 (2).
19. (with Giovanni Peccati) "Gaussian limits for vectors valued multiple stochastic integrals", 2005, Seminaire de Probabilites XXXVIII, Lecture Notes in Mathematics, pag.
247-262.
18. (with Nathalie Eisenbaum) "A question on squared fractional Brownian motions", 2005, Seminaire de Probabilites XXXVIII, Lecture Notes in Mathematics, pag.282-289.
2004:
17. " Ito-Skorohod stochastic equations and applications to finance", 2004, Journal of Applied Mathematics and Stochastic Analysis, 4, pag. 359-369.
16. (with Soledad Torres) "The Euler scheme for a class of anticipating equations", 2004, Random Operators and Stochastic Equations, 12(3), pag. 211-224.
15. (with Samy Tindel et Frederi Viens) "Sharp Gaussian regularity on the circle and application to the fractional stochastic heat equation", 2004, Journal of Functional Analysis", 217(2), pag. 280-313.
14. (with M'Hamed Eddahbi, Ramon Lacayo, Josep Lluis Sole et Josep Vives) "Regularity for the local times for multidimensional fractional Brownian motion with $N$
parameters", 2005, Stochastic Analysis and Applications, 23(2), pag. 383-400.
13."Martingale type stochastic calculus for anticipating integrals", 2004, Bernoulli, 10(2), pag. 315-323.
2003:
12. (with Frederi Viens) "Ito formula and local time for the fractional Brownian sheet", 2003, Electronic Journal of Probability, 8, paper 14, pag. 1-31
11. (with Xavier Bardina et Maria Jolis) "Weak approximation of the fractional Brownian motion sheet", 2003, Statistics and Probability Letters, 65(4), pag. 317-329.
10. (with Samy Tindel et Frederi Viens) "Stochastic evolution equations with fractional Brownian motion", 2003, Probability Theory and Related Fields, 127, pag. 186-204.
9. (with Xavier Bardina et Maria Jolis) "Convergence in law to the multiple fractional integrals", 2003, Stochastic Processes and their Applications, 105, 315-344.
2000-2002:
8. "Weak convergence to the fractional Brownian sheet in Besov spaces", 2002, Bulletin of the Brazilian Mathematical Society, 34(13), pag. 1-12.
7. (with Hassan Lakhel et Youssef Ouknine ) "Besov regularity for the indefinite Skorohod integral with respect to the fractional Brownian motion", Stochastics and Stochastics Reports, 74(3-4): 597-615, 2002.
6. (with Josep Vives) "The indefinite Skorohod integral as integrator on the Poisson space ", Random Operators and Stochastic Equations, 10 (1): 29-46, 2002.
5. (with Laure Coutin et David Nualart) ``The Tanaka formula for the fractional Brownian motion'', Stochastic Processes and their Applications, 94(2): 301-315, 2001.
4. (with Josep Vives ) ``Anticipating Stratonovich integral for the Azema martingales'', Stochastic Analysis and Applications, 20 (3): 673-692, 2002.
3. (with Nicolas Privault) ``Skorohod and pathwise stochastic calculus with respect to an L$^2$ process'', Random Operators and Stochastic Equations, 8 (3): 201-224, 2000.
2. ``Ito type stochastic calculus for some anticipating processes driven by a Skorohod integral process'', Annals of the University of Bucharest, Mathematics, 48 (1), 1999.
1. (with M. Tudor) ``Pseudo almost periodic solutions of a class of stochastic differential equations'', Mathematical Reports, 1(51), 1999