Brownian motion and random walks on manifolds

Nicolas Th. Varopoulos

Annales de l'institut Fourier (1984)

  • Volume: 34, Issue: 2, page 243-269
  • ISSN: 0373-0956

Abstract

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We develop a procedure that allows us to “descretise” the Brownian motion on a Riemannian manifold. We construct thus a random walk that is a good approximation of the Brownian motion.

How to cite

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Varopoulos, Nicolas Th.. "Brownian motion and random walks on manifolds." Annales de l'institut Fourier 34.2 (1984): 243-269. <http://eudml.org/doc/74631>.

@article{Varopoulos1984,
abstract = {We develop a procedure that allows us to “descretise” the Brownian motion on a Riemannian manifold. We construct thus a random walk that is a good approximation of the Brownian motion.},
author = {Varopoulos, Nicolas Th.},
journal = {Annales de l'institut Fourier},
keywords = {Riemannian manifold; approximation of the Brownian motion},
language = {eng},
number = {2},
pages = {243-269},
publisher = {Association des Annales de l'Institut Fourier},
title = {Brownian motion and random walks on manifolds},
url = {http://eudml.org/doc/74631},
volume = {34},
year = {1984},
}

TY - JOUR
AU - Varopoulos, Nicolas Th.
TI - Brownian motion and random walks on manifolds
JO - Annales de l'institut Fourier
PY - 1984
PB - Association des Annales de l'Institut Fourier
VL - 34
IS - 2
SP - 243
EP - 269
AB - We develop a procedure that allows us to “descretise” the Brownian motion on a Riemannian manifold. We construct thus a random walk that is a good approximation of the Brownian motion.
LA - eng
KW - Riemannian manifold; approximation of the Brownian motion
UR - http://eudml.org/doc/74631
ER -

References

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  1. [1]N. TH. VAROPOULOS, Brownian Motion and Transient Groups, Ann. Inst. Fourier, 33-2 (1983), 241-261. Zbl0498.60012MR84i:58130
  2. [2]H. P. MCKEAN JE., Stochastic Integrals, Academic Press, 1969. Zbl0191.46603
  3. [3]N. TH. VAROPOULOS, Potential Theory and Diffusion on Riemannian Manifolds, Conference on Harmonic analysis in honor of Antoni Zygmund. (Wadsworth). 
  4. [4]T. J. LYONS and H. P. MCKEAN, Winding of the Plane Brownian Motion (preprint). Zbl0541.60075
  5. [5]J. CHEEGER and D. G. EBIN, Comparison Theorems in Riemannian Geometry, North-Holland, 1975. Zbl0309.53035MR56 #16538
  6. [6]J. MILNOR, A Note on Curvature and Fundamental Group, J. Diff. Geometry, 2 (1968), 1-7. Zbl0162.25401MR38 #636
  7. [7]P. BALDI, N. LOHOUÉ et J. PEYRIÈRE, C.R.A.S., Paris, t. 285 (A), 1977, 1103-1104. Zbl0376.60072
  8. [8]S. T. YAU, On the Heat Kernel of a Complete Riemannian Manifold, J. Math. Pure et Appl., 57 (1978), 191-201. Zbl0405.35025MR81b:58041
  9. [9]J. CHEEGER and S. T. YAU, A Lower Bound for the Heat Kernel, Comm. Pure and Appl. Math., vol. XXXIV (1981), 465-480. Zbl0481.35003MR82i:58065
  10. [10]H. DONNELLY and P. LI, Lower Bounds for the Eigen Values of Negatively Curved Manifolds, Math. Z., 172 (1980), 29-40. Zbl0413.58020MR81j:58080
  11. [11]S. Y. CHENG, P. LI, and S. T. YAU, On the Upper Estimate of the Heat Kernel of a Complete Riemannian Manifold, Amer. J. of Math., Vol. 103(5) (1980), 1021-1063. Zbl0484.53035MR83c:58083
  12. [12]L. V. AHLFORS, Conformal Invariants, New-York, McGraw-Hill. Zbl0049.17702
  13. [13]N. TH. VAROPOULOS, Random Walks on Soluble Groups, Bull. Sci. Math., 2e série, 107 (1983), 337-344. Zbl0532.60009MR85e:60076
  14. [14]M. GROMOV, Structures Métriques pour les variétés Riemanniennes, Cedic/Fernand Nathan (1981). Zbl0509.53034MR85e:53051
  15. [15]Y. GUIVARC'H, C.R.A.S., Paris, t. 292 (I) (1981), 851-853. 
  16. [16]J. VAUTHIER, Théorèmes d'annulation, Bull. Sc. math., 2e série, 103 (1979), 129-177. Zbl0419.35044
  17. [17]H. DONNELLY, Spectral geometry, Math Z., 169 (1979), 63-76. Zbl0432.58022
  18. [18]N. TH. VAROPOULOS, C.R.A.S., t. 297 (I), p. 585. Zbl0535.30038

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