Horizontal martingales in vector bundles
Séminaire de probabilités de Strasbourg, Volume 36  (2002), p. 419-456
@article{SPS_2002__36__419_0,
     author = {Arnaudon, Marc and Thalmaier, Anton},
     title = {Horizontal martingales in vector bundles},
     journal = {S\'eminaire de probabilit\'es de Strasbourg},
     publisher = {Springer - Lecture Notes in Mathematics},
     volume = {36},
     year = {2002},
     pages = {419-456},
     zbl = {1046.58013},
     mrnumber = {1971603},
     language = {en},
     url = {http://www.numdam.org/item/SPS_2002__36__419_0}
}
Arnaudon, Marc; Thalmaier, Anton. Horizontal martingales in vector bundles. Séminaire de probabilités de Strasbourg, Volume 36 (2002) , pp. 419-456. http://www.numdam.org/item/SPS_2002__36__419_0/

[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. | Numdam | MR 1725710 | Zbl 0946.60030

[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. | MR 1618537 | Zbl 0916.58045

[3] _, Stability of stochastic differential equations in manifolds, Séminaire de Probabilités, XXXII, Springer, Berlin, 1998, pp. 188-214. | Numdam | MR 1655151 | Zbl 0918.60040

[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. | Numdam | MR 837212 | Zbl 0592.58046

[5] R.O. Bauer, Characterizing Yang-Mills fields by stochastic parallel transport, J. Funct. Anal. 155 (1998), no. 2, 536-549. | MR 1624498 | Zbl 0913.60042

[6] _, Yang-Mills fields and stochastic parallel transport in small geodesic balls, Stochastic Process. Appl. 89 (2000), no. 2, 213-226. | MR 1780287 | Zbl 1049.58034

[7] N. Berline, E. Getzler, and M. Vergne, Heat kernels and Dirac operators, Springer-Verlag, Berlin, 1992. | MR 1215720 | Zbl 0744.58001

[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. | MR 1189367

[9] B.K. Driver and A. Thalmaier, Heat equation derivative formulas for vector bundles, J. Funct. Anal., to appear. | MR 1837533 | Zbl 0983.58018

[10] K.D. Elworthy, Y. Le Jan, and Xue-Mei Li, On the geometry of diffusion operators and stochastic flows, Springer-Verlag,Berlin, 1999. | MR 1735806 | Zbl 0942.58004

[11] M. Emery, En marge de l'exposé de Meyer "Géométrie différentielle stochastique", Séminaire de Probabilités, XVI, Supplément, Springer, Berlin, 1982, pp. 208-216. | Numdam | MR 658726 | Zbl 0547.58042

[12] _, Stochastic calculus in manifolds, Springer-Verlag, Berlin, 1989. With an appendix by P.-A. Meyer. | Zbl 0697.60060

[13] H.B. Lawson, Jr. and M.-L. Michelsohn, Spin geometry, Princeton University Press, Princeton, NJ, 1989. | MR 1031992 | Zbl 0688.57001

[14] P. Malliavin, Stochastic Jacobi fields, Partial differential equations and geometry (Proc. Conf., Park City, Utah, 1977), Dekker, New York, 1979, pp. 203-235. | MR 535595 | Zbl 0447.58035

[15] _, Stochastic analysis, Springer-Verlag, Berlin, 1997.

[16] P.-A. Meyer, Géometrie différentielle stochastique (bis), Séminaire de Probabilités, XVI, Supplément, Springer, Berlin, 1982, pp. 165-207. | Numdam | MR 658725 | Zbl 0539.58039

[17] J. Roe, Elliptic operators, topology and asymptotic methods, second ed., Longman, Harlow, 1998. | MR 1670907 | Zbl 0919.58060

[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. | MR 1110171 | Zbl 0726.58055

[19] K. Yano and S. Ishihara, Tangent and cotangent bundles: differential geometry, Marcel Dekker Inc., New York, 1973, Pure and Applied Mathematics, No. 16. | MR 350650 | Zbl 0262.53024