Convergence of martingales on manifolds of negative curvature

R. W. R. Darling

Annales de l'I.H.P. Probabilités et statistiques (1985)

  • Volume: 21, Issue: 2, page 157-175
  • ISSN: 0246-0203

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Darling, R. W. R.. "Convergence of martingales on manifolds of negative curvature." Annales de l'I.H.P. Probabilités et statistiques 21.2 (1985): 157-175. <http://eudml.org/doc/77254>.

@article{Darling1985,
author = {Darling, R. W. R.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {martingale on a Riemannian manifold; sectional curvatures; existence of non-constant bounded harmonic functions},
language = {eng},
number = {2},
pages = {157-175},
publisher = {Gauthier-Villars},
title = {Convergence of martingales on manifolds of negative curvature},
url = {http://eudml.org/doc/77254},
volume = {21},
year = {1985},
}

TY - JOUR
AU - Darling, R. W. R.
TI - Convergence of martingales on manifolds of negative curvature
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1985
PB - Gauthier-Villars
VL - 21
IS - 2
SP - 157
EP - 175
LA - eng
KW - martingale on a Riemannian manifold; sectional curvatures; existence of non-constant bounded harmonic functions
UR - http://eudml.org/doc/77254
ER -

References

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  1. [1] R.W.R. Darling, Martingales on manifolds and geometric Ito calculus. Ph. D. Thesis, University of Warwick, 1982. 
  2. [2] R.W.R. Darling, Martingales in manifolds—definition, examples and behaviour under maps. Springer Lecture Notes in Math., t. 921, 1982, p. 217-236. Zbl0482.58035MR658727
  3. [3] R.W.R. Darling, Convergence of martingales on a Riemannian manifold. Publ. R. I. M. S., Kyoto University, t. 19, 1983, p. 753-763. Zbl0532.58033MR716974
  4. [4] A. Debiard, B. Gaveau and E. Mazet, Temps de sortie des boules normales et minoration locale de λ1. C. R. Acad. Sci. Paris, t. 278A, 1974, p. 795-798. Zbl0274.53039MR341635
  5. [5] K.D. Elworthy, Stochastic differential equations on manifolds. London Math. Soc. Lecture Notes, t. 70, Cambridge U. P., 1982. Zbl0514.58001MR675100
  6. [6] M. Emery, Convergence des martingales dans les variétés. Actes du Colloque Laurent Schwartz (Astérisque), 1984, to appear. Zbl0575.60047MR816759
  7. [7] R.E. Greene and H. Wu, Function theory on manifolds which possess a pole. Springer Lecture Notes in Math., t. 699, 1979. Zbl0414.53043MR521983
  8. [8] K. Ichihara, Curvature, goedesics and the Brownian motion on a Riemannian manifold. II: explosion properties, Nagoya Math. J., t. 87, 1982, p. 115-125. Zbl0514.58039MR676590
  9. [9] N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes. North Holland, 1981. Zbl0495.60005MR637061
  10. [10] P.A. Meyer, Géométrie stochastique sans larmes. Sém. de Probabilités XV, 1979/1980, Springer Lecture Notes in Math., t. 850, 1981, p. 44-102. Zbl0459.60046MR622555
  11. [11] P.A. Meyer, Le théorème de convergence des martingales dans les variétés riemanniennes. Sém. Prob. XVII, Springer Lecture Notes in Math., t. 986, 1983, p. 187-193. Zbl0525.60056MR770410
  12. [12] J.-J. Prat, Étude asymptotique et convergence angulaire du mouvement brownien sur une variété à courbure négative. C. R. A. S., t. 280, ser. A, 1975, p. 1539-1542. Zbl0309.60052MR388557
  13. [13] D.W. Stroock and S.R.S. Varadhan, Multidimensional diffusion processes. Springer-Verlag, 1979. Zbl0426.60069MR532498
  14. [14] D. Sullivan, The Dirichlet problem at infinity for a negatively curved manifold. J. Differential Geometry, t. 18, 1983, p. 723-732. Zbl0541.53037MR730924
  15. [15] W.A. Zheng, Sur la convergence des martingales dans une variété riemannienne. Zeit. fur Wahrsch., t. 63, 1983, p. 511-515. MR705621
  16. [16] K. Ito and H.P. McKean, Diffusion processes and their sample paths. Springer, Berlin, 1965. Zbl0127.09503

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