Fabrice Baudoin





I am  Professor of Mathematics at Purdue University.

Research Interests:

  • Diffusions semigroups, Diffusion processes and Differential Geometry
  • Functional inequalities with a geometric content
  • Malliavin Calculus and Gaussian Processes
  • Financial Mathematics
Research partially funded by NSF award DMS 0907326

  1. With Cheng Ouyang and Xuejing Zhang: Varadhan estimates for rough differential equations driven by fractional Brownian motions, 2013, Arxiv preprint

  2. With Cheng Ouyang and Xuejing Zhang: Smoothing effect of rough differential equations driven by fractional Brownian motions, 2013, Arxiv preprint

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

  4. With Jing Wang: Curvature dimension inequalities and subelliptic heat kernel gradient bounds on contact manifolds,  To appear in Potential Analysis, 2013,  Arxiv preprint

  5. With Michel Bonnefont,  Nicola Garofalo, Isidro H. Munive: Volume and distance comparison theorems for sub-Riemannian manifolds , Arxiv preprint

  6. With Bumsik Kim: Sobolev, Poincare and isoperimetric inequalities for subelliptic diffusion operators satisfying a generalized curvature dimension inequality, To appear in Revista Matematica Iberoamericana, 2012,  Arxiv preprint

  7. With Jing Wang: The subelliptic heat kernel on the CR sphere, To appear in Math. Zeit., 2012,  Arxiv preprint

  8. 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

  9. With Michel Bonnefont: Sub-Riemannian balls in CR Sasakian manifolds, 2011, To appear in the Proceedings of the AMS,  Arxiv preprint

  10. With Rodrigo Bañuelos: Martingale transforms and their projection operators on manifolds , 2011 , To appear in Potential Analysis,  Arxiv preprint

  11. With Maria Gordina and Tai Melcher: Quasi-invariance for heat kernel measures on sub-Riemannian infinite-dimensional Heisenberg groups, 2011, Arxiv preprint,  To appear in the Transactions of the AMS

  12. 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.

  13. With Nicola Garofalo: A note on boundedness of Riesz transform for some subelliptic operators,  Arxiv preprint, International Mathematics Research Notices, rnr271, 24 pages, doi:10.1093/imrn/rnr271, 2012.

  14. With Cheng Ouyang and Samy Tindel: Upper bounds for the density of solutions of stochastic differential equations driven by fractional Brownian motions, 2012, To appear in the Annales de l'IHP,  Arxiv preprint

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

  16. With Alice Vatamanelu: A note on lower bounds estimates for the Neumann eigenvalues of  manifolds with positive Ricci curvature, To appear in Potential Analysis, 2011, Arxiv preprint

  17. With Michel Bonnefont and Nicola Garofalo: A sub-Riemannian curvature-dimension inequality, volume doubling property and the Poincaré inequality, To appear in Math. Ann. 2013, Arxiv preprint

  18. 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

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

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

  21. Stochastic Taylor expansions and heat kernels asymptotics, Accepted for publication in ESAIMPS, 2010, Arxiv preprint

  22. With Nicola Garofalo: Curvature-dimension inequalities and Ricci lower bounds for sub-Riemannian manifolds with transverse symmetries, Arxiv preprint

  23. 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

  24. 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).

  25. 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).

  26. 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).

  27. 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).

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

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

  30. 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).

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

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

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

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

  35. 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).

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

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

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

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

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

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

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

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

  44. 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).

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

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

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