Vitesse de convergence vers l'état d'équilibre pour des dynamiques markoviennes non höldériennes
Kondah, Abdelaziz ; Maume, Véronique ; Schmitt, Bernard
Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997), p. 675-695 / Harvested from Numdam
@article{AIHPB_1997__33_6_675_0,
     author = {Kondah, Abdelaziz and Maume, V\'eronique and Schmitt, Bernard},
     title = {Vitesse de convergence vers l'\'etat d'\'equilibre pour des dynamiques markoviennes non h\"old\'eriennes},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {33},
     year = {1997},
     pages = {675-695},
     mrnumber = {1484537},
     zbl = {0913.60046},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIHPB_1997__33_6_675_0}
}
Kondah, Abdelaziz; Maume, Véronique; Schmitt, Bernard. Vitesse de convergence vers l'état d'équilibre pour des dynamiques markoviennes non höldériennes. Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997) pp. 675-695. http://gdmltest.u-ga.fr/item/AIHPB_1997__33_6_675_0/

[Bi1] G. Birkoff, Extensions of Jentzch's theorem. T.A.M.S., 85, 1957, p. 219-227. | MR 87058 | Zbl 0079.13502

[Bi2] G. Birkoff, Lattice theory (3rd edition), Amer. Math. Soc., 1967. | MR 227053 | Zbl 0153.02501

[Bo] R. Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms., Lect. Notes in Math, 470, 1975, Springer Verlag. | MR 442989 | Zbl 0308.28010

[Ch] N. Chernov, Limit theorems and Markov approximations for chaotic dynamical systems, Probability Theory and Related Fields, 101, 1995, p. 321-362. | MR 1324089 | Zbl 0839.60025

[Co] P. Collet, Some ergodic properties of maps of the interval, Dynamical and disordered systems. R. Bamon, J.M. Gambaudo and S. Martinez ed. - Herman. | MR 1600931 | Zbl 0876.58024

[C, I] P. Collet et S. Isola, On the essential spectrum of the transfert operator for expansive Markov maps, Comm. Math. Phy., 139, 1991, p. 551-557. | MR 1121133 | Zbl 0754.58032

[D] M. Denker, The central limit theorem for dynamical systems, Dynamical Systems and Ergodic Theory, Banach Center Publications, 23, 1989, PWN - Polish Scientific Pulishers, Warsaw. | MR 1102700 | Zbl 0695.60026

[Fe, Sc] P. Ferrero et B. Schmitt, Ruelle Perron Frobenius theorems and projective metrics, Colloque Math. Soc. J. Bolyai Random Fields. Estergom (Hungry), 1979.

[Go] M.I. Gordin, The central limit theorem for stationary processes, Soviet. Math. Dokl., 10, 1969, (5), p. 1174-1176. | MR 251785 | Zbl 0212.50005

[Gor] P. Gora, Properties of invariant measures for piecewise expanding one-dimensional transformations with summable oscillations of derivative, Erg. Th. and Dyn. Syst. 1994, 14, p. 475-492. | MR 1293404 | Zbl 0822.28008

[H, K] F. Hofbauer et G. Keller, Ergodic properties of invariant measures for piecewise monotonic transformations, Math. Zeitschrift, 180, 1982, p. 119-140. | MR 656227 | Zbl 0485.28016

[I, L] I.M. Ibragimov et Y. Linnik, Independant and stationary sequences of random variables, Walters-Noardhoff Pub. Groningen 1971. | MR 322926 | Zbl 0219.60027

[Le] F. Ledrappier, Some properties of absolutely invariant measures on an interval, Erg. Th. and Dyn. Syst., 1, 1981. | MR 627788 | Zbl 0487.28015

[Li1] C. Liverani, Decay of corelations Ann. of Math., 142, 1995, (2), p. 239-301. | MR 1343323 | Zbl 0871.58059

[Li2] C. Liverani, Central limit theorem for deterministic systems, Proceedings of the International Congress on Dynamical Systems, Montevideo 95, Research Notes in Mathematics series, Pittman, 1997. | MR 1460797 | Zbl 0871.58055

[Pa, Po] W. Parry et M. Pollicott, Zeta functions and the periodic orbit structure of hyperbolic dynamics, Asterisque, 187 -188, 1990. | MR 1085356 | Zbl 0726.58003

[Ra] A. Raugi, Théorie spectrale d'un opérateur de transfert sur un espace métrique compact, Ann. Inst. Henri Poincaré, Prob. Stat., 28, (2), 1992, p. 281-309. | Numdam | MR 1162576 | Zbl 0752.60054

[Ru1] D. Ruelle, Thermodynamic formalism., Addison Wesley New-York 1978. | MR 511655

[Ru2] D. Ruelle, Statiscal mechanic of a one dimensionnal lattice gas, Com. Math. Phys., 9, 1978, p. 267-278. | MR 234697 | Zbl 0165.29102

[Sc] B. Schmitt, Existence of acip for expanding maps of the interval, Dynamical Systems and Ergodic Theory Banach Center Publications. Warszaw, 1989. | Zbl 0745.58034

[Si] G. Sinai, Gibbs measures in ergodic theory, Rus. Math. Surveys, 166, 1972, p. 21-69. | MR 399421 | Zbl 0255.28016

[Wa] P. Walters, Invariant measures and equilibrium states for somme mappings which expand distances, Trans. Amer. Math. Soc., 236, 1978, p. 121-153. | MR 466493 | Zbl 0375.28009