|
|
Table of contents for this issue | Previous article | Next article Nicolas Th. VaropoulosBrownian motion and random walks on manifoldsAnnales de l'institut Fourier, 34 no. 2 ( 1984), p. 243-269, doi: 10.5802/aif.972
Article PDF | Reviews MR 85m:58186 | Zbl 0523.60071 | 1 citation in Cedram
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.
[1]N. TH. VAROPOULOS, Brownian Motion and Transient Groups, Ann. Inst. Fourier, 33-2 (1983), 241-261.
Cedram | MR 84i:58130 | Zbl 0498.60012[2]H. P. MCKEAN JE., Stochastic Integrals, Academic Press, 1969. Zbl 0191.46603[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 0541.60075[5]J. CHEEGER and D. G. EBIN, Comparison Theorems in Riemannian Geometry, North-Holland, 1975. MR 56 #16538 | Zbl 0309.53035[6]J. MILNOR, A Note on Curvature and Fundamental Group, J. Diff. Geometry, 2 (1968), 1-7. MR 38 #636 | Zbl 0162.25401[7]P. BALDI, N. LOHOUÉ et J. PEYRIÈRE, C.R.A.S., Paris, t. 285 (A), 1977, 1103-1104. Zbl 0376.60072[8]S. T. YAU, On the Heat Kernel of a Complete Riemannian Manifold, J. Math. Pure et Appl., 57 (1978), 191-201. MR 81b:58041 | Zbl 0405.35025[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 82i:58065 | Zbl 0481.35003[10]H. DONNELLY and P. LI, Lower Bounds for the Eigen Values of Negatively Curved Manifolds, Math. Z., 172 (1980), 29-40. MR 81j:58080 | Zbl 0413.58020[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 83c:58083 | Zbl 0484.53035[12]L. V. AHLFORS, Conformal Invariants, New-York, McGraw-Hill. Zbl 0049.17702[13]N. TH. VAROPOULOS, Random Walks on Soluble Groups, Bull. Sci. Math., 2e série, 107 (1983), 337-344. MR 85e:60076 | Zbl 0532.60009[14]M. GROMOV, Structures Métriques pour les variétés Riemanniennes, Cedic/Fernand Nathan (1981). MR 85e:53051 | Zbl 0509.53034[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 0419.35044[17]H. DONNELLY, Spectral geometry, Math Z., 169 (1979), 63-76. Zbl 0432.58022[18]N. TH. VAROPOULOS, C.R.A.S., t. 297 (I), p. 585. Zbl 0535.30038
|