no. 1
On the functional central limit theorem for stationary processes
Annales de l'I.H.P. Probabilités et statistiques, Tome 36 (2000) no. 1, pp. 1-34. 
@article{AIHPB_2000__36_1_1_0,
     author = {Dedecker, J\'er\^ome and Rio, Emmanuel},
     title = {On the functional central limit theorem for stationary processes},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {1--34},
     publisher = {Gauthier-Villars},
     volume = {36},
     number = {1},
     year = {2000},
     mrnumber = {1743095},
     zbl = {0949.60049},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPB_2000__36_1_1_0/}
}
TY  - JOUR
AU  - Dedecker, Jérôme
AU  - Rio, Emmanuel
TI  - On the functional central limit theorem for stationary processes
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2000
SP  - 1
EP  - 34
VL  - 36
IS  - 1
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPB_2000__36_1_1_0/
LA  - en
ID  - AIHPB_2000__36_1_1_0
ER  - 
%0 Journal Article
%A Dedecker, Jérôme
%A Rio, Emmanuel
%T On the functional central limit theorem for stationary processes
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2000
%P 1-34
%V 36
%N 1
%I Gauthier-Villars
%U http://archive.numdam.org/item/AIHPB_2000__36_1_1_0/
%G en
%F AIHPB_2000__36_1_1_0
Dedecker, Jérôme; Rio, Emmanuel. On the functional central limit theorem for stationary processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 36 (2000) no. 1, pp. 1-34. http://archive.numdam.org/item/AIHPB_2000__36_1_1_0/

[1] A. De Acosta, Moderate deviations for empirical measures of Markov chains: lower bounds, Ann. Probab. 25 (1997) 259-284. | MR | Zbl

[2] P. Ango-Nzé, Critères d'ergodicité de modèles markoviens. Estimation non paramétrique des hypothèses de dépendance, Thèse de doctorat d'université, Université Paris 9, Dauphine, 1994.

[3] P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968. | MR | Zbl

[4] R.C. Bradley, On quantiles and the central limit question for strongly mixing sequences, J. Theor. Probab. 10 (1997) 507-555. | MR | Zbl

[5] X. Chen, Limit theorems for functionals of ergodic Markov chains with general state space, Mem. Amer. Math. Soc. 139 (1999) 664. | MR | Zbl

[6] J. Dedecker, A central limit theorem for stationary random fields, Probab. Theory Relat. Fields 110 (1998) 397-426. | MR | Zbl

[7] B. Delyon, Limit theorem for mixing processes, Tech. Report IRISA, Rennes 1, 546, 1990.

[8] P. Doukhan, P. Massart and E. Rio, The functional central limit theorem for strongly mixing processes, Annales Inst. H. Poincaré Probab. Statist. 30 (1994) 63-82. | Numdam | MR | Zbl

[9] M. Duflo, Algorithmes Stochastiques, Mathématiques et Applications, Springer, Berlin, 1996. | MR | Zbl

[10] A.M. Garsia, A simple proof of E. Hopf's maximal ergodic theorem, J. Math. and Mech. 14 (1965) 381-382. | MR | Zbl

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

[12] M.I. Gordin, Abstracts of Communication, T.1:A-K, International Conference on Probability Theory, Vilnius, 1973.

[13] M.I. Gordin and B.A. LIFŠIC, The central limit theorem for stationary Markov processes, Soviet Math. Dokl. 19 (1978) 392-394. | MR | Zbl

[14] C.C. Heyde, On the central limit theorem and iterated logarithm law for stationary processes, Bull. Austral. Math. Soc. 12 (1975) 1-8. | MR | Zbl

[15] I.A. Ibragimov, A central limit theorem for a class of dependent random variables, Theory Probab. Appl. 8 (1963) 83-89. | MR | Zbl

[16] N. Maigret, Théorème de limite centrale pour une chaîne de Markov récurrente Harris positive, Annales Inst. H. Poincaré Probab. Statist. 14 (1978) 425-440. | Numdam | MR | Zbl

[17] S.P. Meyn and R.L. Tweedie, Markov Chains and Stochastic Stability, Communications and Control Engineering Series, Springer, Berlin, 1993. | MR | Zbl

[18] E. Nummelin, General Irreducible Markov Chains and Nonnegative Operators, Cambridge University Press, London, 1984. | MR | Zbl

[19] V.V. Petrov, Limit Theorems of Probability Theory: Sequences of Independent Random Variables, Oxford University Press, Oxford, 1995. | MR | Zbl

[20] E. Rio, Covariance inequalities for strongly mixing processes, Annales Inst. H. Poincaré Probab. Statist. 29 (1993) 587-597. | Numdam | MR | Zbl

[21] E. Rio, A maximal inequality and dependent Marcinkiewicz-Zygmund strong laws, Ann. Probab. 23 (1995) 918-937. | MR | Zbl

[22] M. Rosenblatt, A central limit theorem and a strong mixing condition, Proc. Nat. Acad. Sci. USA 42 (1956) 43-47. | MR | Zbl

[23] Y.A. Rozanov and V.A. Volkonskii, Some limit theorem for random functions I, Theory Probab. Appl. 4 (1959) 178-197. | MR | Zbl

[24] P. Tuominen and R.L. Tweedie, Subgeometric rates of convergence of f -ergodic Markov chains, Adv. Appl. Probab. 26 (1994) 775-798. | MR | Zbl

[25] G. Viennet, Inequalities for absolutely regular sequences: application to density estimation, Probab. Theor. Related Fields 107 (1997) 467-492. | MR | Zbl

[26] D. Volný, Approximating martingales and the central limit theorem for strictly stationary processes, Stoch. Processes Appl. 44 (1993) 41-74. | MR | Zbl