Martingales on noncompact manifolds : maximal inequalities and prescribed limits
Annales de l'I.H.P. Probabilités et statistiques, Tome 32 (1996) no. 4, pp. 431-454. 
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     author = {Darling, R.W.R.},
     title = {Martingales on noncompact manifolds : maximal inequalities and prescribed limits},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {431--454},
     publisher = {Gauthier-Villars},
     volume = {32},
     number = {4},
     year = {1996},
     mrnumber = {1411268},
     zbl = {0861.58050},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPB_1996__32_4_431_0/}
}
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Darling, R.W.R. Martingales on noncompact manifolds : maximal inequalities and prescribed limits. Annales de l'I.H.P. Probabilités et statistiques, Tome 32 (1996) no. 4, pp. 431-454. http://archive.numdam.org/item/AIHPB_1996__32_4_431_0/

[1] R.L. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc., Vol. 145, 1969, pp. 1-49. | MR | Zbl

[2] R.W.R. Darling, Convergence of martingales on a Riemannian manifold, Publ. Res. Inst. Math. Kyoto Univ., Vol. 19, 1983, pp. 753-763. | MR | Zbl

[3] R.W.R. Darling, Exit probability estimates for martingales in geodesic balls, using curvature, Probability Theory and Related Fields, Vol. 93, 1992, pp. 137-152. | MR | Zbl

[4] R.W.R. Darling, Differential Forms and Connections, Cambridge University Press, 1994. | MR | Zbl

[5] R.W.R. Darling, Constructing gamma-martingales with prescribed limit using backwards SDE, Annals of Probability, Vol. 23, 1995, pp. 1234-1261. | MR | Zbl

[6] M. Emery, Convergence des martingales dans les variétés, Colloque en l'hommage de Laurent Schwartz, Vol. 2, Astérisque 132, Société Mathématique de France, 1985, pp. 47-63. | Numdam | MR | Zbl

[7] M. Emery and P.-A. Meyer, Stochastic Calculus on Manifolds, Springer-Verlag, Berlin, 1989. | Zbl

[8] M. Emery and G. Mokobodzki, Sur le barycentre d'une probabilité dans une variété, Séminaire de Probabilités XXV, Lecture Notes in Mathematics, Vol. 1485, 1991, pp. 220-233. | Numdam | MR | Zbl

[9] R.E. Greene and K. Shiohama, Convex functions on complete noncompact manifolds: topological structure, Invent. Math., Vol. 63, 1981, pp. 129-157. | MR | Zbl

[10] R.E. Greene and H. Wu, Function Theory on Manifolds Which Possess a Pole, Lecture Notes in Mathematics, Vol. 699. | Zbl

[11] R. Hermann, Differential Geometry and the Calculus of Variations, Academic Press, New York, 1968. | MR | Zbl

[12] W.S. Kendall, Martingales on manifolds and harmonic maps, Geometry of Random Motion, R. Durrett and M. Pinsky, eds., Amer. Math. Soc., Providence, 121-157; corrections (with H. Huang) in Stochastics, Vol. 37, 1988, pp. 253-257. | MR | Zbl

[13] W.S. Kendall, Probability, convexity, and harmonic maps with small image I: uniqueness and fine existence, Proc. London Math. Soc., Vol. 61, 1990, pp. 371-406. | MR | Zbl

[14] W.S. Kendall, Convex Geometry and Nonconfluent Γ-martingales I: Tightness and Strict Convexity in Stochastic Analysis, Proceedings, LMS Durham Symposium 1990, M. T. Barlow, N. H. Bingham (eds.), 1991a, pp. 163-178. | MR | Zbl

[15] W.S. Kendall, Convexity and the hemisphere, J. London Math. Soc., (2), Vol. 43, 1991b, pp. 567-576. | MR | Zbl

[16] W.S. Kendall, The Propeller: a counterexample to a conjectured criterion for the existence of certain convex functions, J. London Math. Soc., (2), Vol. 46, 1992, pp. 364-374. | MR | Zbl

[17] W.S. Kendall, Brownian motion and partial differential equations: from the heat equation to harmonic maps, in Proc. ISI 49th Session, Firenze, Vol. 3, 1993, pp. 85-101.

[18] W.S. Kendall, Probability, convexity, and harmonic maps II: smoothness via probabilistic gradient inequalities, Journal of Functional Analysis, Vol. 126, 1994, pp. 228-257. | MR | Zbl

[19] E. Pardoux and S. Peng, Adapted solution of a backward stochastic differential equation, System and Control Letters, Vol. 14, 1990, pp. 55-61. | MR | Zbl

[20] J. Picard, Martingales sur le cercle, Séminaire de Probabilités XXIII, Lecture Notes in Mathematics, Vol. 1372, 1989, pp. 147-160. | Numdam | MR | Zbl

[21] J. Picard, Martingales on Riemannian manifolds with prescribed limit, J. Functional Analysis, Vol. 99, 1991, pp. 223-261. | MR | Zbl

[22] J. Picard, Barycentres et martingales sur une variété, Ann. de l'Institut H. Poincaré, Vol. 30, 1994, pp. 647-702. | Numdam | MR | Zbl

[23] D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, Springer-Verlag, Berlin, 1991. | MR | Zbl