Manifold-valued martingales, changes of probabilities, and smoothness of finely harmonic maps

Marc Arnaudon; Xue-Mei Li; Anton Thalmaier

Annales de l'I.H.P. Probabilités et statistiques (1999)

  • Volume: 35, Issue: 6, page 765-791
  • ISSN: 0246-0203

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Arnaudon, Marc, Li, Xue-Mei, and Thalmaier, Anton. "Manifold-valued martingales, changes of probabilities, and smoothness of finely harmonic maps." Annales de l'I.H.P. Probabilités et statistiques 35.6 (1999): 765-791. <http://eudml.org/doc/77645>.

@article{Arnaudon1999,
author = {Arnaudon, Marc, Li, Xue-Mei, Thalmaier, Anton},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {stochastic calculus on manifolds; -convex geometry; martingales with prescribed terminal value; finely harmonic maps},
language = {eng},
number = {6},
pages = {765-791},
publisher = {Gauthier-Villars},
title = {Manifold-valued martingales, changes of probabilities, and smoothness of finely harmonic maps},
url = {http://eudml.org/doc/77645},
volume = {35},
year = {1999},
}

TY - JOUR
AU - Arnaudon, Marc
AU - Li, Xue-Mei
AU - Thalmaier, Anton
TI - Manifold-valued martingales, changes of probabilities, and smoothness of finely harmonic maps
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1999
PB - Gauthier-Villars
VL - 35
IS - 6
SP - 765
EP - 791
LA - eng
KW - stochastic calculus on manifolds; -convex geometry; martingales with prescribed terminal value; finely harmonic maps
UR - http://eudml.org/doc/77645
ER -

References

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  1. [1] M. Arnaudon, Differentiable and analytic families of continuous martingales in manifolds with connection, Probab. Theory Related Fields108 (1997) 219-257. Zbl0883.60043MR1452557
  2. [2] M. Arnaudon and A. Thalmaier, Complete lifts of connections and stochastic Jacobi fields, J. Math. Pures Appl.77 (1998) 283-315. Zbl0916.58045MR1618537
  3. [3] R.W.R. Darling, Martingales on noncompact manifolds: maximal inequalities and prescribed limits, Annales de l'Institut Henri Poincaré32 (4) (1996) 431-454. Zbl0861.58050MR1411268
  4. [4] J. Eells and L. Lemaire, Another report on harmonic maps, Bull. London Math. Soc.20 (1988) 385-524. Zbl0669.58009MR956352
  5. [5] K.D. Elworthy, Harmonic maps and the non-linear heat equation, Unpublished notes, Warwick, 1993. 
  6. [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. Zbl0881.60052MR1439515
  7. [7] M. Émery, Stochastic Calculus in Manifolds, Springer, 1989. Zbl0697.60060MR1030543
  8. [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. Zbl0675.58042MR1063050
  9. [9] W. Kendall, Probability, convexity, and harmonic maps II: Smoothness via probabilistic gradient inequalities, J. Funct. Anal.126 (1994) 228-257. Zbl0808.60058MR1305069
  10. [10] H. Kunita, Stochastic Flows and Stochastic Differential Equations, Cambridge University Press, 1990. Zbl0743.60052MR1070361
  11. [11] J. Picard, Martingales on Riemannian manifolds with prescribed limits, J. Funct. Anal.99 (1991) 223-261. Zbl0758.60051MR1121614
  12. [12] J. Picard, Barycentres et martingales sur une variété, Annales de l'Institut Henri Poincaré30 (1994) 647-702. Zbl0817.58047MR1302764
  13. [13] D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, 2nd ed., Springer, 1994. Zbl0804.60001MR1303781
  14. [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. Zbl0914.58042MR1622800
  15. [15] K. Yano and S. Ishihara, Tangent and Cotangent Bundles, Marcel Dekker, New York, 1973. Zbl0262.53024MR350650

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