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All issues Volume 16 (2012) ESAIM: PS, 16 (2012) 453-478 References
Issue
ESAIM: PS
Volume 16, 2012
Special Issue: Spring School Mons Random differential equations and Gaussian fields
Page(s) 453 - 478
DOI https://doi.org/10.1051/ps/2011107
Published online 31 October 2012
  1. M.F. Atiyah and R. Bott, A Lefschetz fixed point formula for elliptic complexes. I. Ann. Math. 86 (1967) 374–407. [CrossRef] [Google Scholar]
  2. R. Azencott, Formule de Taylor stochastique et développements asymptotiques d’intégrales de Feynman, in Séminaire de probabilités XVI, edited by J. Azema, M. Yor. Lect. Notes. Math. 921 (1982) 237–284. [CrossRef] [Google Scholar]
  3. R. Azencott, Densité des diffusions en temps petit : développements asymptotiques (part I), Sem. Prob. 18 (1984) 402–498. [Google Scholar]
  4. F. Baudoin, An Introduction to the Geometry of Stochastic Flows. Imperial College Press (2004). [Google Scholar]
  5. F. Baudoin, Brownian Chen series and Atiyah–Singer theorem. J. Funct. Anal. 254 (2008) 301–317. [CrossRef] [MathSciNet] [Google Scholar]
  6. F. Baudoin and L. Coutin, Operators associated with a stochastic differential equation driven by fractional Brownian motions. Stoc. Proc. Appl. 117 (2007) 550–574. [CrossRef] [Google Scholar]
  7. G. Ben Arous, Méthodes de Laplace et de la phase stationnaire sur l’espace de Wiener (French) [The Laplace and stationary phase methods on Wiener space]. Stochastics 25 (1988) 125–153. [CrossRef] [MathSciNet] [Google Scholar]
  8. G. Ben Arous, Développement asymptotique du noyau de la chaleur hypoelliptique hors du cut-locus (French) [Asymptotic expansion of the hypoelliptic heat kernel outside of the cut-locus]. Ann. Sci. Cole Norm. Sup. 21 (1988) 307–331. [Google Scholar]
  9. G. Ben Arous, Développement asymptotique du noyau de la chaleur hypoelliptique sur la diagonale. Ann. Inst. Fourier 39 (1989) 73–99. [CrossRef] [MathSciNet] [Google Scholar]
  10. G. Ben Arous, Flots et séries de Taylor stochastiques. J. Probab. Theory Relat. Fields 81 (1989) 29–77. [CrossRef] [Google Scholar]
  11. G. Ben Arous and R. Léandre, Décroissance exponentielle du noyau de la chaleur sur la diagonale. II (French) [Exponential decay of the heat kernel on the diagonal II] Probab. Theory Relat. Fields 90 (1991) 377–402. [CrossRef] [MathSciNet] [Google Scholar]
  12. N. Berline, E. Getzler and M. Vergne, Heat kernels and Dirac operators, 2nd edition. Grundlehren Text Editions, Springer (2003). [Google Scholar]
  13. J.M. Bismut, The Atiyah–Singer Theorems : A Probabilistic Approach. J. Func. Anal., Part I, II 57 (1984) 329–348. [CrossRef] [Google Scholar]
  14. N. Bourbaki, Groupes et Algèbres de Lie, Chap. 1–3. Hermann (1972). [Google Scholar]
  15. F. Castell, Asymptotic expansion of stochastic flows. Probab. Theory Relat. Fields 96 (1993) 225–239. [CrossRef] [Google Scholar]
  16. K.T. Chen, Integration of paths, Geometric invariants and a generalized Baker-Hausdorff formula. Ann. Math. 65 (1957). [Google Scholar]
  17. S.S. Chern, A simple intrinsic proof of the Gauss-Bonnet theorem for closed Riemannian manifolds. Ann. Math. 45 (1944) 747–752. [CrossRef] [MathSciNet] [Google Scholar]
  18. E.B. Dynkin, Calculation of the coefficients in the Campbell-Hausdorff formula. Dodakly Akad. Nauk SSSR 57 (1947) 323–326, in Russian, English translation (1997). [Google Scholar]
  19. M. Fliess and D. Normand-Cyrot, Algèbres de Lie nilpotentes, formule de Baker-Campbell-Hausdorff et intégrales itérées de K.T. Chen, in Séminaire de Probabilités. Lect. Notes Math. 920 (1982). [Google Scholar]
  20. A. Friedman, Partial differential equations of parabolic type. Prentice-Hall, Inc., Englewood Cliffs, NJ (1964) xiv+347. [Google Scholar]
  21. P. Friz and N. Victoir, Euler estimates for rough differential equations. J. Differ. Equ. 244 (2008) 388–412. [CrossRef] [Google Scholar]
  22. P. Friz and N. Victoir, Multidimensional stochastic processes as rough paths. Theory and Applications, Cambridge Studies in Adv. Math. (2009). [Google Scholar]
  23. B. Gaveau, Principe de moindre action, propagation de la chaleur et estimées sous-elliptiques sur certains groupes nilpotents. Acta Math. 139 (1977) 95–153. [CrossRef] [MathSciNet] [Google Scholar]
  24. E. Getzler, A short proof of the Atiyah–Singer index theorem. Topology 25 (1986) 111–117. [CrossRef] [MathSciNet] [Google Scholar]
  25. P.B. Gilkey, Curvature and the eigenvalues of the Laplacian for elliptic complexes. Adv. Math. 10 (1973) 344–382. [CrossRef] [Google Scholar]
  26. E.P. Hsu, Stochastic Analysis on manifolds. AMS, Providence USA. Grad. Texts Math. 38 (2002). [Google Scholar]
  27. Y. Inahama, A stochastic Taylor-like expansion in the rough path theory. Preprint from Tokyo Institute of Technology (2007) [Google Scholar]
  28. P.E. Kloeden and E. Platen, Numerical solution of stochastic differential equations. Appl. Math. 23 (1992). [Google Scholar]
  29. H. Kunita, Asymptotic self-similarity and short time asymptotics of stochastic flows. J. Math. Sci. Univ. Tokyo 4 (1997) 595–619. [MathSciNet] [Google Scholar]
  30. R. Léandre, Sur le théorème d’Atiyah–Singer. Probab. Theory Relat. Fields 80 (1988) 119–137. [CrossRef] [Google Scholar]
  31. R. Léandre, Développement asymptotique de la densité d’une diffusion dégénérée. Forum Math. 4 (1992) 45–75. [MathSciNet] [Google Scholar]
  32. T. Lyons, Differential equations driven by rough signals. Revista Mathemàtica Iberio Americana 14 (1998) 215–310. [Google Scholar]
  33. T. Lyons and N. Victoir, Cubature on Wiener space. Proc. R. Soc. Lond. A 460 (2004) 169–198. [Google Scholar]
  34. H. McKean and I.M. Singer, Curvature and the eigenvalues of the Laplacian. J. Differ. Geom. 1 (1967) 43–69. [Google Scholar]
  35. P. Malliavin, Stochastic calculus of variations and hypoelliptic operators, in Proc. of Inter. Symp. Stoch. Differ. Equ., Kyoto 1976, edited by Wiley (1978) 195–263. [Google Scholar]
  36. P. Malliavin, Stochastic Analysis. Grundlehren der Mathematischen Wissenschaften 313 (1997). [Google Scholar]
  37. V.K. Patodi, An analytic proof of the Riemann-Roch-Hirzebruch theorem. J. Differ. Geom. 5 (1971) 251–283. [Google Scholar]
  38. C. Reutenauer, Free Lie algebras, London Mathematical Society Monographs. New series 7 (1993). [Google Scholar]
  39. S. Rosenberg, The Laplacian on a Riemannian manifold. London Mathematical Society Student Texts 31 (1997). [Google Scholar]
  40. L.P. Rotschild and E.M. Stein, Hypoelliptic differential operators and Nilpotent groups. Acta Math. 137 (1976) 247–320. [CrossRef] [MathSciNet] [Google Scholar]
  41. D. Stroock and S.R.S. Varadhan, Multidimensional diffusion processes. Springer-Verlag, Berlin, New York. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 233 (1979) xii+338. [Google Scholar]
  42. R.S. Strichartz, The Campbell-Baker-Hausdorff-Dynkin formula and solutions of differential equations. J. Func. Anal. 72. (1987) 320–345. [CrossRef] [Google Scholar]
  43. S. Takanobu, Diagonal short time asymptotics of heat kernels for certain degenerate second order differential operators of Hörmander type. Publ. Res. Inst. Math. Sci. 24 (1988) 169–203. [CrossRef] [MathSciNet] [Google Scholar]
  44. M.E. Taylor, Partial Differential Equations, Basic Theory, 2nd edition. Appl. Math. 23 (1999) [Google Scholar]
  45. M.E. Taylor, Partial Differential Equations, Qualitative Studies of Linear Equations. Appl. Math. Sci. 116 (1996). [Google Scholar]

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