On the functional central limit theorem for stationary processes
Dedecker, Jérôme ; Rio, Emmanuel
Annales de l'I.H.P. Probabilités et statistiques, Tome 36 (2000), p. 1-34 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@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},
     volume = {36},
     year = {2000},
     pages = {1-34},
     mrnumber = {1743095},
     zbl = {0949.60049},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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) pp. 1-34. http://gdmltest.u-ga.fr/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 1428509 | Zbl 0877.60019

[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 233396 | Zbl 0172.21201

[4] R.C. Bradley, On quantiles and the central limit question for strongly mixing sequences, J. Theor. Probab. 10 (1997) 507-555. | MR 1455156 | Zbl 0887.60028

[5] X. Chen, Limit theorems for functionals of ergodic Markov chains with general state space, Mem. Amer. Math. Soc. 139 (1999) 664. | MR 1491814 | Zbl 0952.60014

[6] J. Dedecker, A central limit theorem for stationary random fields, Probab. Theory Relat. Fields 110 (1998) 397-426. | MR 1616496 | Zbl 0902.60020

[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 1262892 | Zbl 0790.60037

[9] M. Duflo, Algorithmes Stochastiques, Mathématiques et Applications, Springer, Berlin, 1996. | MR 1612815 | Zbl 0882.60001

[10] A.M. Garsia, A simple proof of E. Hopf's maximal ergodic theorem, J. Math. and Mech. 14 (1965) 381-382. | MR 209440 | Zbl 0178.38601

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

[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 501277 | Zbl 0395.60057

[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 372954 | Zbl 0287.60035

[15] I.A. Ibragimov, A central limit theorem for a class of dependent random variables, Theory Probab. Appl. 8 (1963) 83-89. | MR 151997 | Zbl 0123.36103

[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 523221 | Zbl 0414.60040

[17] S.P. Meyn and R.L. Tweedie, Markov Chains and Stochastic Stability, Communications and Control Engineering Series, Springer, Berlin, 1993. | MR 1287609 | Zbl 0925.60001

[18] E. Nummelin, General Irreducible Markov Chains and Nonnegative Operators, Cambridge University Press, London, 1984. | MR 776608 | Zbl 0551.60066

[19] V.V. Petrov, Limit Theorems of Probability Theory: Sequences of Independent Random Variables, Oxford University Press, Oxford, 1995. | MR 1353441 | Zbl 0826.60001

[20] E. Rio, Covariance inequalities for strongly mixing processes, Annales Inst. H. Poincaré Probab. Statist. 29 (1993) 587-597. | Numdam | MR 1251142 | Zbl 0798.60027

[21] E. Rio, A maximal inequality and dependent Marcinkiewicz-Zygmund strong laws, Ann. Probab. 23 (1995) 918-937. | MR 1334177 | Zbl 0836.60026

[22] M. Rosenblatt, A central limit theorem and a strong mixing condition, Proc. Nat. Acad. Sci. USA 42 (1956) 43-47. | MR 74711 | Zbl 0070.13804

[23] Y.A. Rozanov and V.A. Volkonskii, Some limit theorem for random functions I, Theory Probab. Appl. 4 (1959) 178-197. | MR 121856 | Zbl 0092.33502

[24] P. Tuominen and R.L. Tweedie, Subgeometric rates of convergence of f -ergodic Markov chains, Adv. Appl. Probab. 26 (1994) 775-798. | MR 1285459 | Zbl 0803.60061

[25] G. Viennet, Inequalities for absolutely regular sequences: application to density estimation, Probab. Theor. Related Fields 107 (1997) 467-492. | MR 1440142 | Zbl 0933.62029

[26] D. Volný, Approximating martingales and the central limit theorem for strictly stationary processes, Stoch. Processes Appl. 44 (1993) 41-74. | MR 1198662 | Zbl 0765.60025