books

Publications





  1. With Jing Wang: Stochastic areas, Windings and Hopf fibrations, Arxiv preprint

  2. Wasserstein contraction properties for hypoellliptic diffusions, Arxiv preprint

  3. With Michel Bonnefont, Reverse Poincare inequalities, Isoperimetry and Riesz transforms in Carnot groups, 2015, To appear in Non Linear Analysis,  Arxiv preprint

  4. With Qi Feng, Log-Sobolev inequalities on the horizontal path space of a totally geodesic foliation, 2015, Arxiv preprint

  5. With Michel Bonnefont, Curvature-dimension estimates for the Laplace-Beltrami operator of a totally geodesic foliation, 2014, To appear in Non Linear Analysis, Arxiv preprint

  6. Sub-Laplacians and hypoelliptic operators on totally geodesic Riemannian foliations, 2014, Insitute Henri Poincare course, To appear as a Chapter in a EMS textbook in mathematics, Arxiv preprint

  7. With Bumsik Kim and Jing Wang: Transverse Weitzenbock formulas and curvature dimension inequalities on Riemannian foliations with totally geodesic leaves, 2014, To appear in Communications in Analysis and Geometry, Arxiv preprint

  8. With Bumsik Kim: The Lichnerowicz-Obata theorem on sub-Riemannian manifolds with transverse symmetries, 2014, To appear in Journal of Geometric Analysis, Arxiv preprint

  9. Diffusion processes and stochastic calculus, 285 pages, EMS textbooks in mathematics,  2014

  10. With Cheng Ouyang: On small time asymptotics for rough differential equations driven by fractional Brownian motions, 2015, Published in "Large Deviations and Asymptotic Methods in Finance", Springer,  Arxiv preprint

  11. Stochastic differential equations driven by loops, To appear in Special Volume of the XI symposium in Probability and Statistic, Progress in Probability, Birkhauser, 2014, Arxiv preprint

  12. Stochastic analysis on sub-Riemannian manifolds with transverse symmetries, To appear in  Annals of Probability, 2014, Arxiv preprint

  13. With Eulalia Nualart, Cheng Ouyang, Samy Tindel: On probability laws of differential systems driven by fractional Brownian motions, 2014, To be published in  Annals of Probability, Arxiv preprint

  14. With Jing Wang: The subelliptic heat kernels of the quaternionic Hopf fibration, Potential Analysis, 41, no 3, 959-982, (2014) Arxiv preprint

  15. Bakry-Emery meet Villani, 2013, Arxiv preprint

  16. With Rodrigo Banuelos: Trace asymptotics for subordinate semigroups,  2013 , Arxiv preprint

  17. With Cheng Ouyang and Xuejing Zhang: Varadhan estimates for rough differential equations driven by fractional Brownian motions, 2013, To appear in Stochastic Processes and their Applications, Arxiv preprint

  18. With Cheng Ouyang and Xuejing Zhang: Smoothing effect of rough differential equations driven by fractional Brownian motions, 2013,  To appear in Annales de l'IHP, Arxiv preprint

  19. With Matthew Cecil: The subelliptic heat kernel on the three-dimensional solvable groups,  To appear in Forum Mathematicum, 2013, Arxiv preprint

  20. With Jing Wang: Curvature dimension inequalities and subelliptic heat kernel gradient bounds on contact manifolds,  Potential Analysis, 40,  2014, 163-193,  Arxiv preprint

  21. With Michel Bonnefont Nicola Garofalo, Isidro H. Munive: Volume and distance comparison theorems for sub-Riemannian manifolds , To appear in Journal of Functional Analysis, 2014, Arxiv preprint

  22. With Bumsik Kim: Sobolev, Poincare and isoperimetric inequalities for subelliptic diffusion operators satisfying a generalized curvature dimension inequality, Revista Matematica Iberoamericana, 30, (2014), 1, 109-131,  Arxiv preprint

  23. With Jing Wang: The subelliptic heat kernel on the CR sphere, Math. Z., 275, (2013), 1-2, 135-150,  Arxiv preprint

  24. With Xuejing Zhang: Taylor expansion for the solution of a stochastic differential equation driven by fractional Brownian motions, Electronic Journal of Probability, Volume 17, Article 51, 1-21, 2012   Link to the article

  25. With Michel Bonnefont: Sub-Riemannian balls in CR Sasakian manifolds, Proceedings of the AMS, 141, (2013), no 11, 3919-3924,  Arxiv preprint

  26. With Rodrigo Banuelos: Martingale transforms and their projection operators on manifolds , Potential Analysis, 38, (2013), no 4, 1071-1089,  Arxiv preprint

  27. With Maria Gordina and Tai Melcher: Quasi-invariance for heat kernel measures on sub-Riemannian infinite-dimensional Heisenberg groups, Transactions of the AMS, 365, (2013), no 8, 4313-4350,   Arxiv preprint

  28. With Michel Bonnefont: Log-Sobolev inequalities for subelliptic operators satisfying a generalized curvature dimension inequality, 2011, Arxiv preprint , Journal of Functional Analysis, Volume 262, Issue 6, 2646-2676, 2012.

  29. With Nicola Garofalo: A note on boundedness of Riesz transform for some subelliptic operatorsArxiv preprint, International Mathematics Research Notices, (2013), no 2, 398-421 .

  30. With Cheng Ouyang and Samy Tindel: Upper bounds for the density of solutions of stochastic differential equations driven by fractional Brownian motions, Annales de l'IHP, (50), 2014, 111-135,  Arxiv preprint

  31. With Cheng Ouyang: Gradient Bounds for Solutions of Stochastic Differential Equations Driven by Fractional Brownian Motions, 2011, Proceedings in honor of Pr. Nualart's 60th birthday, Arxiv preprint

  32. With Alice Vatamanelu: A note on lower bounds estimates for the Neumann eigenvalues of  manifolds with positive Ricci curvature, Potential Analysis, 37, (2012), no 1, 91-101, Arxiv preprint

  33. With Michel Bonnefont and Nicola Garofalo: A sub-Riemannian curvature-dimension inequality, volume doubling property and the Poincare inequality, Math. Ann. 358 (2014), 3-4, 833-860,  Arxiv preprint

  34. With Cheng Ouyang: Small-time kernel expansion for solutions of stochastic differential equations driven by fractional Brownian motions, Stochastic Processes and their Applications, Volume 121, Issue 4, April 2011, Pages 759-792,   Arxiv preprint

  35. With Nicola Garofalo: Perelman's entropy and doubling property on Riemannian manifolds, Journal of Geometric Analysis, 21, 1119-1131, 2011,   Arxiv preprint

  36. Stochastic processes, in The International Encyclopedia of Education, 3rd Edition, edited by Barry McGaw, Penelope Peterson and Eva Baker, Elsevier (2009).

  37. Stochastic Taylor expansions and heat kernels asymptotics, ESAIM: Probability and Statistics/ Volume 16/ January 2012, pp. 453-478 Arxiv preprint

  38. With Nicola Garofalo: Curvature-dimension inequalities and Ricci lower bounds for sub-Riemannian manifolds with transverse symmetries, To appear in Journal of the EMS, Arxiv preprint

  39. With N. O'Connell: Exponential functionals of Brownian motion and class one Whittaker functions, Annales de l'IHP, Probabilites et Statistique, Vol.47, 1096-1120, (2011), Arxiv preprint

  40. With D. Bakry, Michel Bonnefont, B. Qian : Subelliptic Li-Yau estimates on three dimensional model spaces Arxiv preprint , Potential Theory and Stochastics in Albac, Aurel Cornea Memorial Volume (2009).

  41. With Michel Bonnefont: The subelliptic heat kernel on SU(2): Representations, Asymptotics and Gradient bounds Arxiv Preprint, Math. Zeit., Volume 263, Issue 3, Pages 647-672, (2009).

  42. With Martin Hairer, Josef Teichmann: Ornstein-Uhlenbeck processes on Lie groups, Arxiv preprint, Journal of Functional Analysis, Volume 255, Issue 4, Pages 877-890, (2008).

  43. With D. Bakry, M. Bonnefont, D. Chafai: On gradient bounds for the heat kernel on the Heisenberg group Preprint, Journal of Functional Analysis, Volume 255, Issue 8, pp. 1905-1938 (2008).

  44. With Laure Coutin: Self-similarity and fractional Brownian motion on Lie groups, Arxiv Preprint, Electronic Journal of Probability, Vol. 13, pp. 1120-1139, (2008).

  45. With Martin Hairer: A version of Hörmander's theorem for the fractional Brownian motion, Arixv Preprint, Prob. The. Rel. Fields., 139, 373-395, (2007).

  46. With Laure Coutin: Operators associated with a stochastic differential equation driven by fractional brownian motions, Arxiv Preprint, Stochastic Processes and their Applications, 117, Issue 5, pp. 550-574, (2007).

  47. Chen series and Atiyah-Singer theorem, Journal of Functional Analysis, Vol. 254, 2, pp. 301-317 (2008). Link

  48. A Bismut type theorem for subelliptic semigroups, CRAS, 2007, Vol. 34, 12, pp. 765

  49. With Laure Coutin: Volterra Bridges and non-canonical Representations, Markov processes and related fields, Vol. 13, Issue 3, pp. 587-596, (2007). Link

  50. With David Nualart: Notes on the two-dimensional fractional Brownian motion, Annals of Probability, 2006, Vol. 34, 1, 159-180. Link

  51. With Laure Coutin: Etude en temps petit du flot d'equations conduites par des mouvements browniens fractionnaires, in French, Note CRAS, Ser. I 341, 39-42, (2005). Link

  52. An Introduction to the geometry of stochastic flows, Imperial College Press, 140pp, (2005).

  53. The tangent space to a hypoelliptic diffusion and applications, Séminaire de Probabilités,Vol. XXXVIII, LNM 1857, Springer, (2005).

  54. With Josef Teichmann: Hypoellipticity in infinite dimensions and an application in interest rate theory, Annals of Applied Probability, 2005, Vol. 15, 3, 1765-1777. Link

  55. Equations differentielles stochastiques conduites par des lacets dans les groupes de Carnot, in French, CRAS serie I 338, (2004) 719-722.

  56. With Laurent Nguyen-Ngoc: The Financial Value of a Weak Information, Finance and Stochastics, 8, pp. 415-435, (2004). Link

  57. Conditioning and Initial Enlargement of Filtration on a Riemannian Manifold, Annals of Probability, Vol. 32, 3A, 2286-2303, (2004). Link

  58. With David Nualart: Equivalence of Volterra Processes, Stochastic Processes and Their Applications, Vol. 107, 327-350 (2003).Link

  59. Modelling Anticipations on a Financial Market, In Paris-Princeton Lectures on Mathematical Finance, Springer, LNM 1814, (2003) Link

  60. With Michele Thieullen: Pinning Class of the Wiener Measure by a Functional: Related Martingales and Invariance Properties, Probability Theory and Related Fields, Vol. 127, 1-36 (2003), Link

  61. Skew-product decompositions of Brownian motions on manifolds: A probabilistic aspect of Lichnerowicz-Szabo theorem, Bulletin des Sciences Mathématiques, Vol. 126, 481-491, (2002). Link

  62. Conditioned Stochastic Differential Equations and Application to Finance, Stochastic Processes and their Applications, Vol. 100, 109-145, (2002), Link.

  63. With Nicolas Gaussel, How can asset allocation benefit from a complex piece of information ? Link

  64. Further Exponential Generalization of Pitman's 2M-X theorem, Electronic Communications in Probability, Vol. 7, 37-46, (2002), Link.