Free Access
Issue
ESAIM: PS
Volume 6, 2002
Page(s) 33 - 88
DOI https://doi.org/10.1051/ps:2002003
Published online 15 November 2002
  1. N. Bary, A treatise on trigonometric series, Vol. 1. Pergamon Press (1984).
  2. P. Billingsley, Convergence of probability measures. J. Wiley and Sons (1968).
  3. S. Le Borgne, Dynamique symbolique et propriétés stochastiques des automorphismes du tore : cas hyperbolique et quasi-hyperbolique, Ph.D. Thesis. University of Rennes I, France (1997).
  4. S. Le Borgne, Un problème de régularité dans l'équation de cobord, in Sémimaires de probabilités de Rennes. Université de Rennes 1 (1998); http://www.maths.univ-rennes1.fr/csp/1998/index.html
  5. L.A. Bunimovich, N.I. Chernov and Y.G. Sinai, Statistical properties of two-dimensional hyperbolic billiards. Russian Math. Surveys 46 (1991) 47-106. [CrossRef] [MathSciNet]
  6. L.A. Bunimovich and Y.G. Sinai, Statistical properties of Lorentz gaz with periodic configuration of scatterers. Comm. Math. Phys. 78 (1981) 479-497. [CrossRef] [MathSciNet]
  7. N.I. Chernov and Y.G. Sinai, Ergodic properties of certain systems of two-dimensional discs and three-dimensional balls. Russian Math. Surveys 42 (1987) 181-207.
  8. M.I. Gordin, The Central Limit theorem for stationary processes. Soviet Math. Dokl. 10 (1969) 1174-1176.
  9. Y. Katznelson, Ergodic automorphisms of Tn are Bernoulli shifts. Israel J. Math. 10 (1971) 186-195. [CrossRef] [MathSciNet]
  10. R.Z. Khas'minskii, On stochastic processes defined by differential equations with a small parameter (translation). Theory Probab. Appl. 11 (1966) 211-228. [CrossRef]
  11. Y. Kifer, Limit theorem in averaging for dynamical systems. Ergodic Theory Dynam. Systems 15 (1995) 1143-1172. [CrossRef] [MathSciNet]
  12. D.A. Lind, Dynamical properties of quasi hyperbolic toral automorphisms. Ergodic Theory Dynam. Systems 2 (1982) 49-68. [CrossRef]
  13. V.P. Leonov, Quelques applications de la méthode des cumulants à la théorie des processus stochastiques stationnaires (in Russian). Nauka, Moscow (1964).
  14. F. Pène, Applications des propriétés stochastiques des systèmes dynamiques de type hyperbolique : ergodicité du billard dispersif dans le plan, moyennisation d'équations différentielles perturbées par un flot ergodique, Ph.D. Thesis. University of Rennes I, France (2000).
  15. F. Pène, Rates of convergence in the CLT for two-dimensional dispersive billiards. Comm. Math. Phys. 225 (2002) 91-119. [CrossRef] [MathSciNet]
  16. D. Revuz and M. Yor, Continuous martingales and brownian motion. Springer-Verlag (1994).
  17. Y.G. Sinai, Dynamical systems with elastic reflections. Russian Math. Surveys 25 (1970) 137-189. [CrossRef] [MathSciNet]
  18. L.-S. Young, Statistical properties of dynamical systems with some hyperbolicity. Ann. of Math. 147 (1998) 585-650. [CrossRef] [MathSciNet]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.