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Ana Bela Cruzeiro
Permanent member
Degree: Agregação
Grupo de Física Matemática
Complexo Interdisciplinar da Universidade de Lisboa
Av. Prof. Gama Pinto, 2
PT-1649-003 Lisboa
Portugal
Room: B1-14
Phone: +351 217904726
(internal: 34126)
Fax: +351 217954288
Email: abcruz@math.ist.utl.pt
External home page:
http://www.math.ist.utl.pt/ ...
 
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Ana Bela Cruzeiro

Full professor at the Mathematics Department of Instituto Superior Técnico.

Principal investigator in the project "Probabilistic approach to finite and infinite dimensional dynamical systems" (PTDC/MAT/104173/2008).

Curriculum Vitæ (portuguese)

Scientific interests

  • Stochastic analysis
  • Infinite dimensional analysis
  • Malliavin calculus
  • Mathematical physics
  • Euclidean quantum mechanics
  • Probabilistic methods in quantum physics
  • Statistical hydrodynamics

Publications

  • 70. (with M. Arnaudon and X. Chen) "Stochastic Euler-Poincaré reduction".
  • 69. "Stochastic calculus of variations for the diffeomorphisms group", Bulletin des sciences mathématiques 135, 6-7 (2011), p. 557-564.
  • 68. (with M. Arnaudon) "Stochastic Lagrangian flows on some compact manifolds" Stochastics, 84, Issue 2-3 (April 2012), p. 367-381.
  • 67. (with M. Arnaudon and N. Galamba) "Lagrangian Navier-Stokes flows: a stochastic model", J. Phys. A: Math. Theor. 44 (2011), 175501.
  • 66. (with M. Arnaudon) "Lagrangian Navier-Stokes diffusions on manifolds: variational principle and stability", arXiv:1004.2176.
  • 65. (with E. Shamarova) "On a forward-backward stochastic system associated to the Burgers equation", arXiv:1001.3367, Stochastic Analysis and Financial Applications, A. Kohatsu-Higa, N. Privault, S. J. Sheu ed, Birkhauser p.p. 65 (2011).
  • 64. "Hydrodynamics, probability and the geometry of the diffeomorphism group", arXiv:0810.5507, Seminar on Stochastic Analysis, Random Fields and Applications IV, R. C. Dalang. M. Dozzy, F. Russo ed, Birkhauser P.P. 63 (2011).
  • 63. (with E. Shamarova) "Navier-Stokes equations and forward-backward SDEs on the group of diffeomorphisms of the torus", Stoch. Proc. and their Applic. 119 (2009), pp. 4034-4060.
  • 62. (with P. Malliavin) "Renormalized stochastic calculus of variations for a renormalized infinite-dimensional Brownian motion", Stochastics 81, 3-4 (2009), pp. 385-399.
  • 61. (with P. Malliavin) "Stochastic calculus of variations on complex line bundle and construction of unitarizing measures for the Poincaré disk", J. Funct. Anal. 256 (2009), 2, pp. 385-408.
  • 60. (with P. Malliavin) "Nonexistence of infinitesimally invariant measures on loop groups", J. Funct. Anal. 254 (2008), 2, pp. 1974-1987.
  • 59. (with P. Malliavin) "Nonergodicity of Euler fluid dynamics on tori versus positivity of the Arnold-Ricci tensor", J. Funct. Anal, 254 (2008),7, pp. 1903-1925.
  • 58. (with C. J. S. Alves) "Monte-Carlo simulation of stochastic differential systems — a geometrical approach", Stoch. Proc. and their Applic. 118 (2008), pp. 346-367.
  • 57. (with P. Malliavin), "Stochastic parallel transport on the d-dimensional torus", in Stochastic Analysis in Mathematical Physics, ed. A. B. Cruzeiro, G. Ben Arous, Y. Le Jan, J. C. Zambrini, World Scientific 2008.
  • 56. (with P. Malliavin) "Stochastic evolution of inviscid Burgers fluid", in Probability, Geometry and Integrable Systems, MSRI Publications, vol. 55, 2007.
  • 55. (with F. Cipriano) "Variational principle for diffusions on the diffeomorhism group with the H2 metric", in Mathematical Analysis of Random Phenomena, ed. A. B. Cruzeiro, H. Ouerdiane, N. Obata, World Scientific, 2007.
  • 54. (with F. Cipriano), "Navier-Stokes equation and diffusions on the group of homeomorphisms of the torus", Comm. Math. Phys. 275 (2007), pp. 255-269.
  • 53. (with F. Flandoli and P. Malliavin), "Brownian motion on volume preserving diffeomorphisms group and existence of global solutions of 2D stochastic Euler equation", J. Funct. Anal. 242 (1) (2007), pp. 304-326.
  • 52. "Malliavin Calculus", in Encyclopedia of Mathematical Physics, ed. J. P. Françoise, G. Naber, T. S. Tsun, Oxford: Elsevier (2006), v.3, p 383.
  • 51. (with X. Zhang) "Bismut type formulae for diffusion semigroups on Riemannian manifolds", Pot. Anal. 25 (2006), pp. 121-130.
  • 50. (with P. Malliavin) "Numerical approximation of diffusions in Rd using normal charts of a Riemannian manifold", Stoch. Processes Appl. nº 116 (2006), pp. 1088-1095.
  • 49. (with X. Zhang) "Lp gradient estimates of symmetric Markov semigroups for 1<p≤2", Acta Math. Sinica V. 22, nº 1  (2006), pp. 101-104.
  • 48. (with F. Cipriano) "Flows associated with irregular Rd–vector fields", J. Diff. Equations 219 (2005), pp. 183-201.
  • 47. "On some probabilistic estimates of heat kernels and applications", Publicaciones de la Real Sociedad Matemática Española, vol. 9, Proceedings of the XIII Fall Workshop on Geometry and Physics, Murcia, September 2004 (2005).
  • 46. (with X. Zhang) "Ornstein-Uhlenbeck semigroups on Riemannian path spaces", in Recent developments in Stochastic Analysis and Related Topics, Proceedings of the First Sino-German Conference on Stochastic Analysis (a satellite conference of ICM 2002), eds. S. Albeverio, Z-M Ma & M. Roeckner, World Scientific, 2004.
  • 45. "Non adapted transformations of the Wiener measure", in Stochastic Analysis and Mathematical Physics, eds. R. Rebolledo, J. Rezende, J. C. Zambrini, World Scientific (2004).
  • 44. (with X. Zhang) "A Littlewood-Paley type inequality on the path space", in Seminar on Stochastic Analysis, Random Fields and Applications IV, Birhauser P.P. nº 58, eds. R. Dalang, M. Dozzi, F. Russo (2004).
  • 43. (with P. Malliavin and A. Thalmaier) "Geometrization of Monte-Carlo numerical analysis of an elliptic operator: strong approximation", C. R. Acad. Sci., Ser I, 338 (2004), pp. 481-486.
  • 42. (with K-N. Xiang) "On metrics for tangent processes on the path space", in Stochastic Analysis and Related Topics VIII, Birhäuser P.P. nº 53, eds. U. Capar and A. S. Ustunel (2003).
  • 41. (with X. Zhang) "Finite dimensional approximation of Riemannian path space geometry", J. Funct. Anal. 205 (2003), pp. 206-270.
  • 40. (with P. Malliavin) "Riemannian Geometry on the Path Space", in Stoch. Partial Diff. Equations and Applications, Lecture Notes in Pure and Applied Math., Marcel Decker Inc. vol. 227, eds. G. da Prato, L. Tubaro (2002), pp. 133-165.
  • 39. (with P. Malliavin) "Stochastic calculus of variations and Harnack inequality on Riemannian path spaces", C. R. Acad. Sc. Paris, Ser.I, t. 335 (2002), pp. 817-820.
  • 38. (with P. Malliavin) "A class of anticipative tangent processes on the Wiener space", C. R. Acad. Sc. Paris, Ser.I, t. 333 (2001), pp. 353-358.
  • 37. (with P. Malliavin and S. Taniguchi) "Ground state estimations in Gauge theory", Bull. Sci. Math. 125, 6-7 (2001), pp. 623-640.
  • 36. (with S. Fang) "Weak Levi-Civita connection for the damped metric on the Riemannian path space and vanishing of Ricci tensor in adapted differential geometry", J. Funct. Anal. 185 (2001), pp. 681-698.
  • 35. (with S. Fang) "A Weitzenböck formula for the damped Ornstein-Uhlenbeck operator in adapted differential geometry", C. R. Acad. Sc. Paris, t. 332 (2001), pp. 447-452.
  • 34. "Construction of some processes on the Wiener space associated to second order operators", J. Korean Math. Soc. 38, nº 2 (2001), pp. 307-315.
  • 33. (with W. Liming and J. C. Zambrini) "Bernstein processes associated with a Markov process", in Stochastic Analysis and Mathematical Physics, Trends in Mathematics, Birkhäuser, ed. R. Rebolledo (2000).
  • 32. (with P. Malliavin) "Frame bundle of Riemannian Path Space and Ricci tensor in adapted differential geometry", J. Funct. Anal. 177 (2000), pp. 219-253.
  • 31. (with S. Fang and P. Malliavin) "A Probabilistic Weitzenböck formula on Riemannian Path Space", J. Anal. Math. Jerusalem, 80 (2000), pp. 87-100.
  • 30. (with P. Malliavin) "Riesz Transforms, Commutators and Stochastic Integrals", in Harmonic Analysis and Partial Diff. Equations, Chicago Lectures in Mathematics, The Univ. of Chicago Press, 1999, pp. 151-162.
  • 29. (with F. Cipriano) "Flows associated to tangent processes on the Wiener space", J. Funct. Anal. 166, 2 (1999), pp. 310-331.
  • 28. (with P. Malliavin) "Energy Identities and Estimates for Anticipative Stochastic Integrals on a Riemannian Manifold", Stochastic Analysis and Related Topics VI, Birkhäuser PP 42 (1998), pp. 221-234.
  • 27. (with P. Malliavin) "Non Perturbative Construction of Invariant Measure through Confinement by Curvature", J. Math. Pures Appl. 77 (1998), pp. 527-537.
  • 26. (with Z. Haba) "Invariant Measure for a Wave Equation on a Riemannian Manifold", Stochastic Differential and Difference Equations, Birkhäuser Progress in Systems and Control Theory 23 (1997), pp. 35-42.
  • 25. (with S. Fang) "An L2-Estimate for Riemannian Anticipative Stochastic Integrals", J. Funct. Anal. 143, 2 (1997), pp. 400-414.
  • 24. (with P. Malliavin) "Renormalized Differential Geometry and Path Space: Structural Equation, Curvature" J. Funct. Anal. 139, 1 (1996), pp. 119-181.
  • 23. (with Z. Haba and J. C. Zambrini) "Bernstein diffusions and Euclidean Quantum Field Theory", Proceedings Monte Verità Meeting, eds. E. Bolthausen, F. Russo, Birkhäuser (1995) (P.P. nº 36).
  • 22. (with A. Brandão) "Singular differential operators and associated processes", in Stochastic Processes, Physics and Geometry II, eds. S. Albeverio, U. Cattaneo, D. Merlini, World Sc. (1995).
  • 21. (with S. Fang) "Une inegalité L2 pour des integrales stochastiques anticipatives sur une variété Riemanniene", C. R. Acad. Sc. Paris, t. 321, Ser. I (1995), pp. 1245-1250.
  • 20. (with P. Malliavin) "Courbures de l’espace de Probabilité d’un Brownien Riemannien", C. R. Acad. Sc. Paris, t. 320, ser. I (1995), pp. 603-607.
  • 19. (with J. C. Zambrini) "Malliavin Calculus and Euclidean Quantum Mechanics II - Variational Principle for Infinite Dimensional Processes", J. Funct. Anal. 130, nº 2 (1995), pp. 450-476.
  • 18. (with P. Malliavin) "Repère Mobile et Géometrie Riemannienne sur les espaces des chemins", C. R. Acad. Sc. Paris, t. 319, ser. I (1994), pp. 859-864.
  • 17. (with J. C. Zambrini) "Euclidean Quantum Mechanics: an outline", Proceedings NATO ASI, Stochastic Analysis and Applications in Physics, ed. L. Streit, Kluwer-Acad. Publ. (1994), pp. 59-97.
  • 16. (with J. C. Zambrini) "Ornstein-Uhlenbeck processes as Bernstein diffusions", Proceedings of the Conference on Stochastic Analysis (Barcelona), Birkhäuser, Boston, Inc. (1993) (P.P. nº 32).
  • 15. (with J. C. Zambrini) "Feynman's functional calculus and stochastic calculus of variations", in Stochastic Analysis and Applications, eds. A. B. Cruzeiro and J. C. Zambrini, Birkhäuser (1991) (P.P. nº 26).
  • 14. (with J. C. Zambrini) "Malliavin Calculus and Euclidean Quantum Mechanics, I - Functional Calculus", J. Funct. Anal., vol. 96, nº 1 (1991), pp. 62-95.
  • 13. "Invariant measures in hydrodynamic systems with random perturbations", in Dynamics and Stochastic Processes, eds. R. Lima, L. Streit, R. Vilela Mendes, Springer-Verlag (1990).
  • 12. (with S. Albeverio) "Global flows with invariant (Gibbs) measures for Euler and Navier-Stokes two dimensional fluids" Comm. Math. Phys. 129 (1990), pp. 431-444.
  • 11. "Flows in infinite dimensions and associated transformations of Gaussian measures", in Stochastic Methods in Mathematics and Physics, eds. R. Gielerak and W. Karwowski, World Sc. (1989).
  • 10. "Invariant measures for Euler and Navier-Stokes systems", in Stochastic Analysis, Path Integration and Dynamics, eds. K. D. Elworthy and J. C. Zambrini, Pitman Res. Notes in Math. Ser. 200 (1989).
  • 9. "Solutions et mesures invariantes pour des équations d'évolution stochastiques du type Navier-Stokes", Expo. Math. 7 (1989), pp. 73-82.
  • 8. "Processus sur l’espace de Wiener associés à des opérateurs élliptiques à coefficients dans certains espaces de Sobolev", J. Funct. Anal. 72, nº 2 (1987), pp. 346-367.
  • 7. "Estimations capacitaires sur l’espace de Wiener, I", Bull. Sc. Math., ser. II, 110 (1986), pp. 139-147.
  • 6. "Diffusions sur l'espace de Wiener", C. R. Acad. Sc. Paris, t. 302, ser. I, nº 8 (1986), pp. 295-298.
  • 5. "Unicité de solutions d’équations différentielles sur l’espace de Wiener", J. Funct. Anal. 58 (1985),  pp. 335-347.
  • 4. "Equations différentielles sur l'espace de Wiener et formules de Cameron-Martin non linéaires", J. Funct. Anal. 54 (1983), pp. 206-227.
  • 3. "Equations différentielles ordinaires: non explosion et mesures quasi-invariantes", J. Funct. Anal. 54 (1983), pp. 193-205.
  • 2. "Convergence au bord pour les fonctions harmoniques dans Rd de la classe de Sobolev Wd,1", C. R. Acad. Sc. Paris, t. 294 (1982), pp. 71-74.
  • 1. "Convergence quasi partout dans des domaines paraboliques des fonctions d'intégrale de Dirichlet finie", C. R. Acad. Sc. Paris, t. 294 (1982), pp. 13-16.

Books (as editor)

  • (with J. C. Zambrini)  Stochastic Analysis and Mathematical Physics (Proceedings of the Lisbon Conference 1999), Birkhäuser, Boston, Inc., P.P. 50 (2001).
  • (with J. C. Zambrini) Stochatic Analysis and Applications (Proceedings of the Lisbon Conference 1989), Birkhäuser, Boston, Inc., P.P. 26 (1991).
  • (with H. Ouerdiane, N. Obata) Mathematical Analysis of Random Phenomena, World Scientific (2007).
  • (with G. Ben Arous, Y. Le Jan, J. C. Zambrini), Stochastic Analysis in Mathematical Physics, World Scientific (2008).