Stochastic methods and differential geometry

K. David Elworthy

Séminaire Bourbaki (1980-1981)

  • Volume: 23, page 95-110
  • ISSN: 0303-1179

How to cite

top

Elworthy, K. David. "Stochastic methods and differential geometry." Séminaire Bourbaki 23 (1980-1981): 95-110. <http://eudml.org/doc/109983>.

@article{Elworthy1980-1981,
author = {Elworthy, K. David},
journal = {Séminaire Bourbaki},
keywords = {Brownian motion; Laplace Beltrami operator; path integral techniques; heat flow; harmonic manifolds; harmonic maps; stochastic differential equations},
language = {eng},
pages = {95-110},
publisher = {Springer-Verlag},
title = {Stochastic methods and differential geometry},
url = {http://eudml.org/doc/109983},
volume = {23},
year = {1980-1981},
}

TY - JOUR
AU - Elworthy, K. David
TI - Stochastic methods and differential geometry
JO - Séminaire Bourbaki
PY - 1980-1981
PB - Springer-Verlag
VL - 23
SP - 95
EP - 110
LA - eng
KW - Brownian motion; Laplace Beltrami operator; path integral techniques; heat flow; harmonic manifolds; harmonic maps; stochastic differential equations
UR - http://eudml.org/doc/109983
ER -

References

top
  1. [1] H. Airault - Subordination de processus dans le fibré tangent et formes harmoniques, C.R. Acad. Sc. Paris, t. 282(14 juin 1976), Sér. A, 1311-1314. Zbl0336.53029MR420740
  2. [2] L. Arnold - Stochastic Differential Equations : Theory and Applications, Wiley-Interscience1974. Zbl0278.60039MR443083
  3. [3] R. Azencott - Behaviour of diffusion semi-groups at infinity, Bull. Soc. Math. France102(1974), 193-240. Zbl0293.60071MR356254
  4. [4] A.-L. Besse - Manifolds all of whose geodesics are closed, Springer-Verlag1978 (Ergebnisse der Mathematik, 93). Zbl0387.53010MR496885
  5. [5] R. Carmona and B. Simon - Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems, V : lower bounds and path integrals, to appear in Comm. Math. Phys.. Zbl0464.35085MR623152
  6. [6] S.-Y. Cheng and S.-T. Yau - Differential equations on Riemannian manifolds and their geometric applications, Comm. Pur. Appl. Math.28(1975), 333-354. Zbl0312.53031MR385749
  7. [7] A. Debiard, B. Gaveau and E. Mazet - Théorèmes de comparaison en géométrie riemannienne, Publ. RIMS. Kyoto Univ. 12(1976), 391-425. Zbl0382.31007MR431294
  8. [8] J. Dodziuk - Maximum principle for parabolic inequalities and the heat flow on open manifolds, Preprint, Mathematics Institute, Oxford University. MR711862
  9. [9] J. Eells and L. Lemaire - A report on harmonic maps, Bull. London Math. Soc.10(1978), 1-68. Zbl0401.58003MR495450
  10. [10] R.-P. Feynman and A.-R. Hibbs - Quantum mechanics and path integrals, McGraw-Hill1965. Zbl0176.54902
  11. [11] A. Friedman - Stochastic Differential Equations and Applications, Vols. 1, 2, Academic Press1975. Zbl0323.60056MR494490
  12. [12] A. Friedman and M. Pinsky (Eds.) - Stochastic Analysis, Academic Press1978. Zbl0436.00019MR517230
  13. [13] K. Ichihara - Curvature, geodesics and the Brownian motion on a Riemannian manifold, I and II, Preprint, Dept. of Applied Sciences, Faculty of Engineering, Kyushu University. 
  14. [14] N. Ikeda and S. Watanabe - A comparison theorem for solutions of stochastic differential equations and its applications, Osaka J. Math.14(1977), 619-633. Zbl0376.60065MR471082
  15. [15] N. Ikeda and S. Watanabe - Stochastic differential equations and diffusion processes, Kodansha - John Wiley, to appear. Zbl0684.60040
  16. [16] K. Itô (Ed.) - Proceedings of the International Symposium on Stochastic Differential Equations, John Wiley and Sons, 1979, Review by D. Williams - Bull. London Math. Soc.12(1980), 141-146. MR535998
  17. [17] K. Itô and H.-P. McKean - Diffusion Processes and their Sample Paths, Springer-Verlag1965. Zbl0127.09503
  18. [18] P. Malliavin - Géométrie différentielle stochastique, Séminaire de Mathématiques Supérieures, Univ. de Montréal, 1978. Zbl0393.60062MR540035
  19. [19] E.-J. McShane - Stochastic Calculus and Stochastic Models, Academic Press1974. Zbl0292.60090MR443084
  20. [20] P.-A. Meyer - Un cours sur les intégrales stochastiques, Séminaire de probabilités X, Lecture Notes in Math., vol. 511, Springer-Verlag1976, 245-400. Zbl0374.60070MR501332
  21. [21] D. Michel - Comparaison des notions de variétés riemanniennes globalement harmoniques et fortement harmoniques, C. R. Acad. Sc. Paris, t 282(1976), Sér. A, 1007-1010. Zbl0332.53030MR417986
  22. [22] M. Pinsky - Stochastic Riemannian geometry, in Probabilistic Analysis and related topics, vol. 1, A.T. Bharucha Reid (Ed.), Academic Press1978. Zbl0452.60083MR501385
  23. [23] J.-J. Prat - Etude asymptotique et convergence angulaire du mouvement brownien sur une variété à courbure négative, C. R. Acad. Sc. Paris, t 280(1975), Sér. A, 1539-1542. Zbl0309.60052MR388557
  24. [24] L. Schwartz - Semi-martingales sur les variétés et martingales conformes sur les variétés analytiques complexes, Lect. Notes in Math.780, Springer-Verlag1980. Zbl0433.60047MR575167
  25. [25] B. Simon - Functional Integration and Quantum Physics, Academic Press1979. Zbl0434.28013MR544188
  26. [26] J. Vauthier - Théorèmes d'annulation et de finitude d'espaces de 1-formes harmoniques sur une variété de Riemann ouverte, Bull. Sc. Math.103(1979), 129-177. Zbl0419.35044MR533895
  27. [27] D. Williams (Ed.) - Stochastic Integrals : Proceedings of the L.M.S. Durham Symposium 1980, to appear in Lect. Notes in Math., Springer-Verlag. Zbl0444.00014MR620983
  28. [28] D. Williams - Review of "Multidimensional diffusion processes" , by D.W. Stroock and S.R.S. Varadhan, Bull. A.M.S.2(1980), 496-503. 
  29. [29] H. Wu - An elementary method in the study of non-negative curvature, Acta Math.142(1979), 57-78. Zbl0403.53022MR512212
  30. [30] S.-T. Yau - Harmonic functions on complete Riemannian manifolds, Comm. Pur. Appl. Math.28(1975), 201-228. Zbl0291.31002MR431040
  31. [31] S.-T. Yau - On the heat kernel of a complete Riemannian manifold, J. Math. pures et appl.57(1978), 191-201. Zbl0405.35025MR505904

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.