Horizontal martingales in vector bundles

Marc Arnaudon; Anton Thalmaier

Séminaire de probabilités de Strasbourg (2002)

  • Volume: 36, page 419-456

How to cite


Arnaudon, Marc, and Thalmaier, Anton. "Horizontal martingales in vector bundles." Séminaire de probabilités de Strasbourg 36 (2002): 419-456. <http://eudml.org/doc/114104>.

author = {Arnaudon, Marc, Thalmaier, Anton},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {stochastic calculus on manifolds; manifold-valued semimartingales; horizontal martingales; Yang-Mills connection},
language = {eng},
pages = {419-456},
publisher = {Springer - Lecture Notes in Mathematics},
title = {Horizontal martingales in vector bundles},
url = {http://eudml.org/doc/114104},
volume = {36},
year = {2002},

AU - Arnaudon, Marc
AU - Thalmaier, Anton
TI - Horizontal martingales in vector bundles
JO - Séminaire de probabilités de Strasbourg
PY - 2002
PB - Springer - Lecture Notes in Mathematics
VL - 36
SP - 419
EP - 456
LA - eng
KW - stochastic calculus on manifolds; manifold-valued semimartingales; horizontal martingales; Yang-Mills connection
UR - http://eudml.org/doc/114104
ER -


  1. [1] M. Arnaudon, Xue-Mei Li , and A. Thalmaier, Manifold-valued martingales, changes ofprobabilities, and smoothness of finely harmonic maps, Ann. Inst. H. Poincaré Probab. Statist.35 (1999), no. 6, 765-791. Zbl0946.60030MR1725710
  2. [2] M. Arnaudon and A. Thalmaier, Complete lifts of connections and stochastic Jacobi fields, J. Math. Pures Appl. (9) 77 (1998), no. 3, 283-315. Zbl0916.58045MR1618537
  3. [3] _, Stability of stochastic differential equations in manifolds, Séminaire de Probabilités, XXXII, Springer, Berlin, 1998, pp. 188-214. Zbl0918.60040MR1655151
  4. [4] R. Azencott, Une approche probabiliste du théorème de l'indice (Atiyah-Singer) (d'après J.-M. Bismut), Astérisque (1986), no. 133-134, 7-18, Seminar Bouibaki, Vol. 1984/85. Zbl0592.58046MR837212
  5. [5] R.O. Bauer, Characterizing Yang-Mills fields by stochastic parallel transport, J. Funct. Anal.155 (1998), no. 2, 536-549. Zbl0913.60042MR1624498
  6. [6] _, Yang-Mills fields and stochastic parallel transport in small geodesic balls, Stochastic Process. Appl.89 (2000), no. 2, 213-226. Zbl1049.58034MR1780287
  7. [7] N. Berline, E. Getzler, and M. Vergne, Heat kernels and Dirac operators, Springer-Verlag, Berlin, 1992. Zbl0744.58001MR1215720
  8. [8] M. Campanino, Stochastic parallel displacement of tensors, Probabilistic methods in mathematical physics (Siena, 1991), World Sci. Publishing, River Edge, NJ, 1992, pp. 127-139. MR1189367
  9. [9] B.K. Driver and A. Thalmaier, Heat equation derivative formulas for vector bundles, J. Funct. Anal., to appear. Zbl0983.58018MR1837533
  10. [10] K.D. Elworthy, Y. Le Jan, and Xue-Mei Li, On the geometry of diffusion operators and stochastic flows, Springer-Verlag,Berlin, 1999. Zbl0942.58004MR1735806
  11. [11] M. Emery, En marge de l'exposé de Meyer "Géométrie différentielle stochastique", Séminaire de Probabilités, XVI, Supplément, Springer, Berlin, 1982, pp. 208-216. Zbl0547.58042MR658726
  12. [12] _, Stochastic calculus in manifolds, Springer-Verlag, Berlin, 1989. With an appendix by P.-A. Meyer. Zbl0697.60060
  13. [13] H.B. Lawson, Jr. and M.-L. Michelsohn, Spin geometry, Princeton University Press, Princeton, NJ, 1989. Zbl0688.57001MR1031992
  14. [14] P. Malliavin, Stochastic Jacobi fields, Partial differential equations and geometry (Proc. Conf., Park City, Utah, 1977), Dekker, New York, 1979, pp. 203-235. Zbl0447.58035MR535595
  15. [15] _, Stochastic analysis, Springer-Verlag, Berlin, 1997. 
  16. [16] P.-A. Meyer, Géometrie différentielle stochastique (bis), Séminaire de Probabilités, XVI, Supplément, Springer, Berlin, 1982, pp. 165-207. Zbl0539.58039MR658725
  17. [17] J. Roe, Elliptic operators, topology and asymptotic methods, second ed., Longman, Harlow, 1998. Zbl0919.58060MR1670907
  18. [18] S. Stafford, A stochastic criterion for Yang-Mills connections, Diffusion processes and related problems in analysis, Vol. I (Evanston, IL, 1989), Birkhäuser Boston, Boston, MA, 1990, pp. 313-322. Zbl0726.58055MR1110171
  19. [19] K. Yano and S. Ishihara, Tangent and cotangent bundles: differential geometry, Marcel Dekker Inc., New York, 1973, Pure and Applied Mathematics, No. 16. Zbl0262.53024MR350650

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