Brownian motion and random walks on manifolds
Annales de l'Institut Fourier, Tome 34 (1984) no. 2, pp. 243-269.

On développe une procédure qui nous permet de discrétiser le mouvement brownien d’une variété riemannienne. On obtient ainsi une marche aléatoire qui est une bonne approximation du mouvement brownien.

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.

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     author = {Varopoulos, Nicolas Th.},
     title = {Brownian motion and random walks on manifolds},
     journal = {Annales de l'Institut Fourier},
     pages = {243--269},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {34},
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     year = {1984},
     doi = {10.5802/aif.972},
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Varopoulos, Nicolas Th. Brownian motion and random walks on manifolds. Annales de l'Institut Fourier, Tome 34 (1984) no. 2, pp. 243-269. doi : 10.5802/aif.972. https://aif.centre-mersenne.org/articles/10.5802/aif.972/

[1]N. Th. Varopoulos, Brownian Motion and Transient Groups, Ann. Inst. Fourier, 33-2 (1983), 241-261. | Numdam | MR | Zbl

[2]H. P. Mckean Je., Stochastic Integrals, Academic Press, 1969. | Zbl

[3]N. Th. Varopoulos, Potential Theory and Diffusion on Riemannian Manifolds, Conference on Harmonic analysis in honor of Antoni Zygmund. (Wadsworth).

[4]T. J. Lyons and H. P. Mckean, Winding of the Plane Brownian Motion (preprint). | Zbl

[5]J. Cheeger and D. G. Ebin, Comparison Theorems in Riemannian Geometry, North-Holland, 1975. | MR | Zbl

[6]J. Milnor, A Note on Curvature and Fundamental Group, J. Diff. Geometry, 2 (1968), 1-7. | MR | Zbl

[7]P. Baldi, N. Lohoué et J. Peyrière, C.R.A.S., Paris, t. 285 (A), 1977, 1103-1104. | Zbl

[8]S. T. Yau, On the Heat Kernel of a Complete Riemannian Manifold, J. Math. Pure et Appl., 57 (1978), 191-201. | MR | Zbl

[9]J. Cheeger and S. T. Yau, A Lower Bound for the Heat Kernel, Comm. Pure and Appl. Math., vol. XXXIV (1981), 465-480. | MR | Zbl

[10]H. Donnelly and P. Li, Lower Bounds for the Eigen Values of Negatively Curved Manifolds, Math. Z., 172 (1980), 29-40. | MR | Zbl

[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. | MR | Zbl

[12]L. V. Ahlfors, Conformal Invariants, New-York, McGraw-Hill. | Zbl

[13]N. Th. Varopoulos, Random Walks on Soluble Groups, Bull. Sci. Math., 2e série, 107 (1983), 337-344. | MR | Zbl

[14]M. Gromov, Structures Métriques pour les variétés Riemanniennes, Cedic/Fernand Nathan (1981). | MR | Zbl

[15]Y. Guivarc'H, C.R.A.S., Paris, t. 292 (I) (1981), 851-853.

[16]J. Vauthier, Théorèmes d'annulation, Bull. Sc. math., 2e série, 103 (1979), 129-177. | Zbl

[17]H. Donnelly, Spectral geometry, Math Z., 169 (1979), 63-76. | Zbl

[18]N. Th. Varopoulos, C.R.A.S., t. 297 (I), p. 585. | Zbl

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