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

 Access to full text

 Full (PDF)

1. [1] J. Aaronson, An Introduction to Infinite Ergodic Theory, Mathematical Surveys and Monographs, vol. 50, American Mathematical Society, 1997. Zbl0882.28013MR1450400
2. [2] J. Aaronson, M. Denker, The Poincaré series of $C\setminus Z$, Ergodic Theory Dynam. Systems19 (1999) 1-20. Zbl0920.30036MR1676950
3. [3] J. Aaronson, M. Denker, Local limit theorems for partial sums of stationary sequences generated by Gibbs–Markov maps, Stochastics and Dynamics1 (2001) 193-237. Zbl1039.37002MR1840194
4. [4] J. Aaronson, B. Weiss, Remarks on the tightness of cocycles, Colloq. Math.8485 (2000) 363-376. Zbl0980.28010MR1784202
5. [5] J.F. Alves, S. Luzzatto, V. Pinheiro, Markov structures and decay of correlations for non-uniformly expanding dynamical systems, Preprint, 2002. Zbl1134.37326
6. [6] S. Bochner, R.S. Phillips, Absolutely convergent Fourier expansions for non-commutative normed rings, Ann. Math.43 (1942) 409-418. Zbl0060.27204MR7939
7. [7] L. Breiman, Probability, Addison-Wesley, 1968. Zbl0174.48801MR229267
8. [8] A. Broise, Transformations dilatantes de l'intervalle et théorèmes limites, Astérisque238 (1996) 1-109. Zbl0988.37032MR1634271
9. [9] H. Bruin, S. Luzzatto, S. van Strien, Decay of correlations in one-dimensional dynamics, Ann. Sci. École Norm. Sup.36 (2003) 621-646. Zbl1039.37021MR2013929
10. [10] J.-P. Conze, S. Le Borgne, Méthode de martingales et flot géodésique sur une surface de courbure constante négative, Ergodic Theory Dynam. Systems21 (2) (2001) 421-441. Zbl0983.37034MR1827112
11. [11] D. Dolgopyat, Limit theorems for partially hyperbolic systems, Trans. Amer. Math. Soc.356 (2004) 1637-1689. Zbl1031.37031MR2034323
12. [12] W. Feller, An Introduction to Probability Theory and its Applications, vol. 2, Wiley Series in Probability and Mathematical Statistics, Wiley, 1966. Zbl0219.60003MR210154
13. [13] J. Frenk, On Banach Algebras, Renewal Measures and Regenerative Processes, CWI Tract, vol. 38, Centrum voor Wiskunde en Informatica, Amsterdam, 1987. Zbl0624.60099MR906870
14. [14] S. Gouëzel, Central limit theorem and stable laws for intermittent maps, Probab. Theory Related Fields128 (2004) 82-122. Zbl1038.37007MR2027296
15. [15] S. Gouëzel, Regularity of coboundaries for non uniformly expanding Markov maps, Preprint, 2004. Zbl1087.37005
16. [16] S. Gouëzel, Sharp polynomial bounds for the decay of correlations, Israel J. Math.139 (2004) 29-65. Zbl1070.37003MR2041223
17. [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. Zbl0649.60041MR937957
18. [18] H. Hennion, Sur un théorème spectral et son application aux noyaux lipschitziens, Proc. Amer. Math. Soc.118 (1993) 627-634. Zbl0772.60049MR1129880
19. [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. Zbl0219.60027MR322926
20. [20] C.T. Ionescu-Tulcea, G. Marinescu, Théorie ergodique pour des classes d'opérations non complètement continues, Ann. Math.47 (1950) 140-147. Zbl0040.06502MR37469
21. [21] J. Komlós, A generalization of a problem of Steinhaus, Acta Math. Acad. Sci. Hungar.18 (1967) 217-229. Zbl0228.60012MR210177
22. [22] S. Le Borgne, F. Pène, Décorrélation multiple pour certains systèmes quasi-hyperboliques. Applications, Preprint. Zbl1090.37018
23. [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. Zbl0871.58055MR1460797
24. [24] C. Liverani, B. Saussol, S. Vaienti, A probabilistic approach to intermittency, Ergodic Theory Dynam. Systems19 (1999) 671-685. Zbl0988.37035MR1695915
25. [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. Zbl0428.28014MR572015
26. [26] M. Pollicott, R. Sharp, Invariance principles for interval maps with an indifferent fixed point, Comm. Math. Phys.229 (2002) 337-346. Zbl1074.37007MR1923178
27. [27] A. Raugi, Étude d’une transformation – non uniformément hyperbolique de l’intervalle $[0,1[$, Bull. Soc. Math. France132 (2004) 81-103. Zbl1049.37018MR2075917
28. [28] B. Rogozin, Asymptotic behavior of the coefficients in Levi–Wiener theorems on absolutely converging trigonometric series, Siberian Math. J.14 (1973) 917-923. Zbl0286.42005MR342940
29. [29] B. Rogozin, Asymptotic behavior of the coefficients of functions of power series and Fourier series, Siberian Math. J.17 (1977) 492-498. Zbl0353.42002MR481860
30. [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. Zbl0518.60033MR704569
31. [31] W. Rudin, Functional Analysis, International Series in Pure and Applied Mathematics, McGraw-Hill, 1991. Zbl0867.46001MR1157815
32. [32] O. Sarig, Subexponential decay of correlations, Invent. Math.150 (2002) 629-653. Zbl1042.37005MR1946554
33. [33] D. Szász, T. Varjú, Local limit theorem for Lorentz process and its recurrence in the plane, Ergodic Theory Dynam. Systems24 (2004) 257-278. Zbl1115.37009MR2041271
34. [34] L.-S. Young, Statistical properties of dynamical systems with some hyperbolicity, Ann. of Math. (2)147 (1998) 585-650. Zbl0945.37009MR1637655
35. [35] L.-S. Young, Recurrence times and rates of mixing, Israel J. Math.110 (1999) 153-188. Zbl0983.37005MR1750438
36. [36] R. Zweimüller, Stable limits for probability preserving maps with indifferent fixed points, Stochastics and Dynamics3 (2003) 83-99. Zbl1035.37001MR1971188

1. Viviane Baladi, Aïcha Hachemi, A local limit theorem with speed of convergence for euclidean algorithms and diophantine costs