Horizontal martingales in vector bundles

Marc Arnaudon; Anton Thalmaier

Séminaire de probabilités de Strasbourg (2002)

  • Volume: 36, page 419-456

How to cite

top

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

@article{Arnaudon2002,
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},
}

TY - JOUR
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 -

References

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.