Empirical invariance principle for ergodic torus automorphisms; Genericity

Stochastics and Dynamics

Volumn 8, Issue 2, 2008, Pages 173-195

  Durieu, Olivier ^a   Jouan, Philippe ^a  

^a Université de Rouen Normandie   (France)

Author keywords

Distribution function; Empirical process; Functional central limit theorem; Genericity; Morse function; Multiple mixing; Partially hyperbolic dynamical system

Indexed keywords

EID: 46249103744     PISSN: 02194937     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219493708002287     Document Type: Article

References (13)

1. M. Berger and B. Gostiaux, Géométric Différentielle: Variétés, Courbes et Surfaces 2nd edn. (Presses Universitaires de France, 1992).
2. P. Billingsley, Convergence of Probability Measures (John Wiley & Sons, 1968).
3. S. Borovkova, R. Burton and H. Dehling, Limit theorems for functionals of mixing processes with applications to U-statistics and dimension estimation, Trans. Amer. Math. Soc. 353 (2001) 4261-4318.
4. R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Mathematics, Vol. 470 (Springer-Verlag, 1975).
5. P. Collet, S. Martinez and B. Schmitt, Asymptotic distribution of tests for expanding maps of the interval, Erg. Th. Dyn. Syst. 24 (2004) 707-722.
6. J. Dedecker and C. Prieur, An empirical central limit theorem for dependent sequences, Stoch. Process. Appl. 117 (2007) 121-142.
7. H. Dehling and W. Philipp, Empirical process techniques for dependent data, in Empirical Process Techniques for Dependent Data (Birkhäuser, 2002), pp. 3-113.
8. M. W. Hirsch, Differential Topology, Graduate Texts in Mathematics, No. 33 (Springer-Verlag, 1976).
9. S. Le Borgne, Dynamique symbolique et propriétés stochastiques des automorphismes du tore: Cas hyperbolique et quasi hyperbolique, Ph.D. thesis, Université de Rennes 1, 1997.
10. S. Le Borgne, Exemples de systèmes dynamiques quasi-hyperboliques à décorrélations lentes, http://perso.univ-rennes1.fr/stephane.leborgne/.
11. S. Le Borgne and F. Pène, Vitesse dans le théorème limite central pour certains systèmes dynamiques quasi-hyperboliques, Bull. Soc. Math. France 133 (2005) 395-417.
12. D. A. Lind, Dynamical properties of quasihyperbolic toral automorphisms, Erg. Th. Dyn. Syst. 2 (1982) 49-68.
13. J. Milnor, Morse Theory, Based on lecture notes by M. Spivak and R. Wells, Annals of Mathematics Studies, No. 51 (Princeton Univ. Press, 1963).