Berry-Esseen theorem and local limit theorem for non uniformly expanding maps

Gouëzel, Sébastien

doi:10.1016/j.anihpb.2004.09.002

Gouëzel, Sébastien

Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 6, pp. 997-1024

Zbl | 3 citations dans Numdam

DOI : 10.1016/j.anihpb.2004.09.002

@article{AIHPB_2005__41_6_997_0,
     author = {Gou\"ezel, S\'ebastien},
     title = {Berry-Esseen theorem and local limit theorem for non uniformly expanding maps},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {997--1024},
     year = {2005},
     publisher = {Elsevier},
     volume = {41},
     number = {6},
     doi = {10.1016/j.anihpb.2004.09.002},
     zbl = {02231405},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpb.2004.09.002/}
}

TY  - JOUR
AU  - Gouëzel, Sébastien
TI  - Berry-Esseen theorem and local limit theorem for non uniformly expanding maps
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2005
SP  - 997
EP  - 1024
VL  - 41
IS  - 6
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.anihpb.2004.09.002/
DO  - 10.1016/j.anihpb.2004.09.002
LA  - en
ID  - AIHPB_2005__41_6_997_0
ER  -

%0 Journal Article
%A Gouëzel, Sébastien
%T Berry-Esseen theorem and local limit theorem for non uniformly expanding maps
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2005
%P 997-1024
%V 41
%N 6
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.anihpb.2004.09.002/
%R 10.1016/j.anihpb.2004.09.002
%G en
%F AIHPB_2005__41_6_997_0

Gouëzel, Sébastien. Berry-Esseen theorem and local limit theorem for non uniformly expanding maps. Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 6, pp. 997-1024. doi: 10.1016/j.anihpb.2004.09.002

Bibliographie
Cité par

[1] J. Aaronson, An Introduction to Infinite Ergodic Theory, Mathematical Surveys and Monographs, vol. 50, American Mathematical Society, 1997. | Zbl | MR

[2] J. Aaronson, M. Denker, The Poincaré series of $C ∖ Z$ , Ergodic Theory Dynam. Systems 19 (1999) 1-20. | Zbl | MR

[3] J. Aaronson, M. Denker, Local limit theorems for partial sums of stationary sequences generated by Gibbs-Markov maps, Stochastics and Dynamics 1 (2001) 193-237. | Zbl | MR

[4] J. Aaronson, B. Weiss, Remarks on the tightness of cocycles, Colloq. Math. 8485 (2000) 363-376. | Zbl | MR

[5] J.F. Alves, S. Luzzatto, V. Pinheiro, Markov structures and decay of correlations for non-uniformly expanding dynamical systems, Preprint, 2002.

[6] S. Bochner, R.S. Phillips, Absolutely convergent Fourier expansions for non-commutative normed rings, Ann. Math. 43 (1942) 409-418. | Zbl | MR

[7] L. Breiman, Probability, Addison-Wesley, 1968. | Zbl | MR

[8] A. Broise, Transformations dilatantes de l'intervalle et théorèmes limites, Astérisque 238 (1996) 1-109. | Zbl | MR | Numdam

[9] H. Bruin, S. Luzzatto, S. Van Strien, Decay of correlations in one-dimensional dynamics, Ann. Sci. École Norm. Sup. 36 (2003) 621-646. | Zbl | MR | Numdam

[10] J.-P. Conze, S. Le Borgne, Méthode de martingales et flot géodésique sur une surface de courbure constante négative, Ergodic Theory Dynam. Systems 21 (2) (2001) 421-441. | Zbl | MR

[11] D. Dolgopyat, Limit theorems for partially hyperbolic systems, Trans. Amer. Math. Soc. 356 (2004) 1637-1689. | Zbl | MR

[12] W. Feller, An Introduction to Probability Theory and its Applications, vol. 2, Wiley Series in Probability and Mathematical Statistics, Wiley, 1966. | Zbl | MR

[13] J. Frenk, On Banach Algebras, Renewal Measures and Regenerative Processes, CWI Tract, vol. 38, Centrum voor Wiskunde en Informatica, Amsterdam, 1987. | Zbl | MR

[14] S. Gouëzel, Central limit theorem and stable laws for intermittent maps, Probab. Theory Related Fields 128 (2004) 82-122. | Zbl | MR

[15] S. Gouëzel, Regularity of coboundaries for non uniformly expanding Markov maps, Preprint, 2004.

[16] S. Gouëzel, Sharp polynomial bounds for the decay of correlations, Israel J. Math. 139 (2004) 29-65. | Zbl | MR

[17] Y. Guivarc'H, J. Hardy, Théorèmes limites pour une classe de chaînes de Markov et applications aux difféomorphismes d'Anosov, Ann. Inst. H. Poincaré Probab. Statist. 24 (1988) 73-98. | Zbl | MR | Numdam

[18] H. Hennion, Sur un théorème spectral et son application aux noyaux lipschitziens, Proc. Amer. Math. Soc. 118 (1993) 627-634. | Zbl | MR

[19] I.A. Ibragimov, Y.V. Linnik, Independent and Stationary Sequences of Random Variables, Wolters-Noordhoff, Groningen, 1971, With a supplementary chapter by I.A. Ibragimov and V.V. Petrov. Translation from the Russian edited by J.F.C. Kingman. | Zbl | MR

[20] C.T. Ionescu-Tulcea, G. Marinescu, Théorie ergodique pour des classes d'opérations non complètement continues, Ann. Math. 47 (1950) 140-147. | Zbl | MR

[21] J. Komlós, A generalization of a problem of Steinhaus, Acta Math. Acad. Sci. Hungar. 18 (1967) 217-229. | Zbl | MR

[22] S. Le Borgne, F. Pène, Décorrélation multiple pour certains systèmes quasi-hyperboliques. Applications, Preprint.

[23] C. Liverani, Central limit theorems for deterministic systems, in: International Conference on Dynamical Systems, Montevideo 1995, Pitman Research Notes in Mathematics, vol. 362, 1996. | Zbl | MR

[24] C. Liverani, B. Saussol, S. Vaienti, A probabilistic approach to intermittency, Ergodic Theory Dynam. Systems 19 (1999) 671-685. | Zbl | MR

[25] C.C. Moore, K. Schmidt, Coboundaries and homomorphisms for nonsingular actions and a problem of H. Helson, Proc. L.M.S. 40 (1980) 443-475. | Zbl | MR

[26] M. Pollicott, R. Sharp, Invariance principles for interval maps with an indifferent fixed point, Comm. Math. Phys. 229 (2002) 337-346. | Zbl | MR

[27] A. Raugi, Étude d’une transformation - non uniformément hyperbolique de l’intervalle $[0, 1 [$ , Bull. Soc. Math. France 132 (2004) 81-103. | Zbl | MR | Numdam

[28] B. Rogozin, Asymptotic behavior of the coefficients in Levi-Wiener theorems on absolutely converging trigonometric series, Siberian Math. J. 14 (1973) 917-923. | Zbl | MR

[29] B. Rogozin, Asymptotic behavior of the coefficients of functions of power series and Fourier series, Siberian Math. J. 17 (1977) 492-498. | Zbl | MR

[30] J. Rousseau-Egele, Un théorème de la limite locale pour une classe de transformations dilatantes et monotones par morceaux, Ann. Probab. 11 (1983) 772-788. | Zbl | MR

[31] W. Rudin, Functional Analysis, International Series in Pure and Applied Mathematics, McGraw-Hill, 1991. | Zbl | MR

[32] O. Sarig, Subexponential decay of correlations, Invent. Math. 150 (2002) 629-653. | Zbl | MR

[33] D. Szász, T. Varjú, Local limit theorem for Lorentz process and its recurrence in the plane, Ergodic Theory Dynam. Systems 24 (2004) 257-278. | Zbl | MR

[34] L.-S. Young, Statistical properties of dynamical systems with some hyperbolicity, Ann. of Math. (2) 147 (1998) 585-650. | Zbl | MR

[35] L.-S. Young, Recurrence times and rates of mixing, Israel J. Math. 110 (1999) 153-188. | Zbl | MR

[36] R. Zweimüller, Stable limits for probability preserving maps with indifferent fixed points, Stochastics and Dynamics 3 (2003) 83-99. | Zbl | MR

Cité par Sources :