Martingales in manifolds. Definition, examples and behaviour under maps

R. W. R. Darling

Séminaire de probabilités de Strasbourg (1982)

  • Volume: S16, page 217-236

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Darling, R. W. R.. "Martingales in manifolds. Definition, examples and behaviour under maps." Séminaire de probabilités de Strasbourg S16 (1982): 217-236. <http://eudml.org/doc/113423>.

@article{Darling1982,
author = {Darling, R. W. R.},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {martingales in manifolds; stochastic process with values in a differential manifold with a linear connection; behaviour of martingales under harmonic maps and affine maps},
language = {eng},
pages = {217-236},
publisher = {Springer - Lecture Notes in Mathematics},
title = {Martingales in manifolds. Definition, examples and behaviour under maps},
url = {http://eudml.org/doc/113423},
volume = {S16},
year = {1982},
}

TY - JOUR
AU - Darling, R. W. R.
TI - Martingales in manifolds. Definition, examples and behaviour under maps
JO - Séminaire de probabilités de Strasbourg
PY - 1982
PB - Springer - Lecture Notes in Mathematics
VL - S16
SP - 217
EP - 236
LA - eng
KW - martingales in manifolds; stochastic process with values in a differential manifold with a linear connection; behaviour of martingales under harmonic maps and affine maps
UR - http://eudml.org/doc/113423
ER -

References

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  1. [1] Bernard, A., Campbell, E.A., & Davie, A.M.. Brownian motion and generalized analytic and inner functions. Ann. Inst. Fourier, 29.1 (1979), 207-228 Zbl0386.30029
  2. [2] Darling, R.W.R.Approximating Ito integrals of differential forms, and mean forward derivatives. (1981) To appear. MR736146
  3. [3] Darling, R.W.R.A Girsanov theorem for diffusions on a manifold (1981) To appear. 
  4. [4] Eells, J. & Lemaire, L.A report on harmonic maps. Bull. London Math. Soc.10 (1978), pp. 1-68. Zbl0401.58003
  5. [5] Eliasson, H.I.Geometry of manifolds of maps. J.Differential GeometryI (1967), 169-194 Zbl0163.43901MR226681
  6. [6] Fuglede, B.Harmonic morphisms between Riemannian manifolds. Ann. Inst. Fourier28.2 (1978), 107-144 Zbl0339.53026MR499588
  7. [7] Greene, R.E. & Wu H., Embedding of open Riemannian manifolds by harmonic functions. Ann. Inst. Fourier25 (1975) 215-235 Zbl0307.31003
  8. [8] Ishihara, ToruA mapping of Riemannian manifolds which preserves harmonic functions. J.Math. Kyoto Univ19-2 (1979) 215-229 Zbl0421.31006MR545705
  9. [9] Kendall, W.S.Brownian motion and a generalized little Picard theorem. To appear 1982. Zbl0507.58017MR682729
  10. [10] Kobayashi, S., & Nomizu, K.Foundation of differential geometry, Vols I and II, Interscience, New York (1963, 1969) Zbl0119.37502
  11. [11] Meyer, P.A.Géometrie stochastique sans larmes. Sem. de Probabilités XV, 1979/1980, SpringerLNM850, pp. 44-102. Zbl0459.60046MR622555
  12. [12] Meyer, P.A.A differential geometric formalism for the Ito calculus. SpringerLNM851 (1981) 256-270 Zbl0457.60031MR620993
  13. [13] Schwartz, L.Semi-martingales sur des variétés, et martingales conformes. (1980) SpringerLNM780. Zbl0433.60047MR575167

Citations in EuDML Documents

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  1. Jean Picard, Martingales sur le cercle
  2. Michel Émery, Wei-An Zheng, Fonctions convexes et semimartingales dans une variété
  3. Michel Émery, Gabriel Mokobodzki, Sur le barycentre d'une probabilité dans une variété
  4. R. W. R. Darling, Convergence of martingales on manifolds of negative curvature
  5. Jean Picard, Calcul stochastique avec sauts sur une variété
  6. M. Hakim-Dowek, Dominique Lépingle, L'exponentielle stochastique des groupes de Lie
  7. Jean Picard, Barycentres et martingales sur une variété
  8. Jean Picard, Stochastic calculus and martingales on trees

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