Manifold-valued martingales, changes of probabilities, and smoothness of finely harmonic maps
Annales de l'I.H.P. Probabilités et statistiques, Volume 35 (1999) no. 6, p. 765-791
@article{AIHPB_1999__35_6_765_0,
     author = {Arnaudon, Marc and Li, Xu-Mei and Thalmaier, Anton},
     title = {Manifold-valued martingales, changes of probabilities, and smoothness of finely harmonic maps},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {35},
     number = {6},
     year = {1999},
     pages = {765-791},
     zbl = {0946.60030},
     mrnumber = {1725710},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1999__35_6_765_0}
}
Arnaudon, Marc; Li, Xue-Mei; Thalmaier, Anton. Manifold-valued martingales, changes of probabilities, and smoothness of finely harmonic maps. Annales de l'I.H.P. Probabilités et statistiques, Volume 35 (1999) no. 6, pp. 765-791. http://www.numdam.org/item/AIHPB_1999__35_6_765_0/

[1] M. Arnaudon, Differentiable and analytic families of continuous martingales in manifolds with connection, Probab. Theory Related Fields 108 (1997) 219-257. | MR 1452557 | Zbl 0883.60043

[2] M. Arnaudon and A. Thalmaier, Complete lifts of connections and stochastic Jacobi fields, J. Math. Pures Appl. 77 (1998) 283-315. | MR 1618537 | Zbl 0916.58045

[3] R.W.R. Darling, Martingales on noncompact manifolds: maximal inequalities and prescribed limits, Annales de l'Institut Henri Poincaré 32 (4) (1996) 431-454. | Numdam | MR 1411268 | Zbl 0861.58050

[4] J. Eells and L. Lemaire, Another report on harmonic maps, Bull. London Math. Soc. 20 (1988) 385-524. | MR 956352 | Zbl 0669.58009

[5] K.D. Elworthy, Harmonic maps and the non-linear heat equation, Unpublished notes, Warwick, 1993.

[6] K.D. Elworthy and X.-M. Li, A class of integration by parts formulae in stochastic analysis I, in: S. Watanabe, Ed., Itô's stochastic Calculus and Probability Theory (dedicated to K. Itô on the occasion of his eightieth birthday), Springer, 1996, 15-30. | MR 1439515 | Zbl 0881.60052

[7] M. Émery, Stochastic Calculus in Manifolds, Springer, 1989. | MR 1030543 | Zbl 0697.60060

[8] W. Kendall, Probability, convexity, and harmonic maps with small image I: Uniqueness and fine existence, Proc. London Math. Soc. (3) 61 (1990) 371-406. | MR 1063050 | Zbl 0675.58042

[9] W. Kendall, Probability, convexity, and harmonic maps II: Smoothness via probabilistic gradient inequalities, J. Funct. Anal. 126 (1994) 228-257. | MR 1305069 | Zbl 0808.60058

[10] H. Kunita, Stochastic Flows and Stochastic Differential Equations, Cambridge University Press, 1990. | MR 1070361 | Zbl 0743.60052

[11] J. Picard, Martingales on Riemannian manifolds with prescribed limits, J. Funct. Anal. 99 (1991) 223-261. | MR 1121614 | Zbl 0758.60051

[12] J. Picard, Barycentres et martingales sur une variété, Annales de l'Institut Henri Poincaré 30 (1994) 647-702. | Numdam | MR 1302764 | Zbl 0817.58047

[13] D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, 2nd ed., Springer, 1994. | MR 1303781 | Zbl 0804.60001

[14] A. Thalmaier and F.-Y. Wang, Gradient estimates for harmonic functions on regular domains in Riemannian manifolds, J. Funct. Anal. 155 (1998) 109-124. | MR 1622800 | Zbl 0914.58042

[15] K. Yano and S. Ishihara, Tangent and Cotangent Bundles, Marcel Dekker, New York, 1973. | MR 350650 | Zbl 0262.53024