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Foliations, the ergodic theorem and Brownian motion. (English) Zbl 0524.58026


MSC:

37A99 Ergodic theory
37C85 Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\)
28C10 Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
58H05 Pseudogroups and differentiable groupoids
60J65 Brownian motion

Citations:

Zbl 0314.57018
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References:

[1] Bowen, R., Unique ergodicity for horocycle foliations, Israel J. Math., 26, 43-67 (1977), (with Brian Marcus) · Zbl 0346.58009
[2] Connes, A., Sur la théorie noncommutative de l’intégration, (Conférence on Foliations and Hyperbolic Geometry. Conférence on Foliations and Hyperbolic Geometry, Plan sur Bex, 1978. Conférence on Foliations and Hyperbolic Geometry. Conférence on Foliations and Hyperbolic Geometry, Plan sur Bex, 1978, Springer Lecture Notes (1978)), New York
[4] Foguel, S. R., Ergodic Theory of Markov Processes (1969), Van Nostrand: Van Nostrand Princeton, N. J · Zbl 0181.44806
[5] Hopf, E., Bull. Amer. Math. Soc., 77, 863-877 (1971)
[6] Ito, K.; McKean, H., Diffusion Processes and Their Sample Paths (1964), Academic Press: Academic Press New York · Zbl 0153.47302
[7] Jacobs, Lecture Notes on Ergodic Theory, Aarhus Notes (1962-1963) · Zbl 0196.31301
[9] Lamperti, J., Stochastic Processes, (Lecture Notes Series, No. 38 (1974), Aarhus Universitet) · Zbl 0113.33502
[10] Malliavin, P., Diffusions et Géométrie Différentielle Globale (August 1975), Centro Internationale Matematico Estivo: Centro Internationale Matematico Estivo Varenne, France
[11] Malliavin, P., Geométrie Différentielle Stochastique (1978), Les Presses de l’Université de Montréal · Zbl 0393.60062
[12] McKean, H., Stochastic Integrals (1969), Academic Press: Academic Press New York · Zbl 0191.46603
[14] Plante, J., Foliations with measure preserving holonomy, Ann. of Math., 102 (1976) · Zbl 0312.57017
[16] Ikeda, N.; Watanabe, S., Stochastic Differential Equation and Diffusion Process (1981), North-Holland: North-Holland Amsterdam
[17] Stroock, D.; Varadham, S., Multidimensional Diffusion Processes, (Ergebnisse Series (1979), Springer: Springer New York)
[18] Sullivan, D., Cycles for the dynamical study of foliated manifolds and complex manifolds, Invent. Math., Serre Volume (1976) · Zbl 0335.57015
[19] Sullivan, D., Ergodic theory at infinity of a discrete group of hyperbolic motions, (Proceedings of Stony Brook Conference on Kleinian Groups (1980), Princeton Univ. Press: Princeton Univ. Press Princeton, N. J)
[20] Yau, Harmonic functions on Riemannian manifolds, Comm. Pure Appl. Math. (1976)
[21] Yosida, K., Functional Analysis (1965), Springer-Verlag: Springer-Verlag Berlin · Zbl 0126.11504
[22] Garnett, L., Functions and Measures Harmonic along Leaves of a Foliation, (Thesis (1981), Dartmouth College: Dartmouth College Hanover, N. H)
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