@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},
year = {2000},
publisher = {Gauthier-Villars},
volume = {36},
number = {1},
mrnumber = {1743095},
zbl = {0949.60049},
language = {en},
url = {https://www.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 - https://www.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 https://www.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. https://www.numdam.org/item/AIHPB_2000__36_1_1_0/
[1] , Moderate deviations for empirical measures of Markov chains: lower bounds, Ann. Probab. 25 (1997) 259-284. | Zbl | MR
[2] , Critères d'ergodicité de modèles markoviens. Estimation non paramétrique des hypothèses de dépendance, Thèse de doctorat d'université, Université Paris 9, Dauphine, 1994.
[3] , Convergence of Probability Measures, Wiley, New York, 1968. | Zbl | MR
[4] , On quantiles and the central limit question for strongly mixing sequences, J. Theor. Probab. 10 (1997) 507-555. | Zbl | MR
[5] , Limit theorems for functionals of ergodic Markov chains with general state space, Mem. Amer. Math. Soc. 139 (1999) 664. | Zbl | MR
[6] , A central limit theorem for stationary random fields, Probab. Theory Relat. Fields 110 (1998) 397-426. | Zbl | MR
[7] , Limit theorem for mixing processes, Tech. Report IRISA, Rennes 1, 546, 1990.
[8] , and , The functional central limit theorem for strongly mixing processes, Annales Inst. H. Poincaré Probab. Statist. 30 (1994) 63-82. | Zbl | MR | Numdam
[9] , Algorithmes Stochastiques, Mathématiques et Applications, Springer, Berlin, 1996. | Zbl | MR
[10] , A simple proof of E. Hopf's maximal ergodic theorem, J. Math. and Mech. 14 (1965) 381-382. | Zbl | MR
[11] , The central limit theorem for stationary processes, Soviet Math. Dokl. 10 (1969) 1174-1176. | Zbl | MR
[12] , Abstracts of Communication, T.1:A-K, International Conference on Probability Theory, Vilnius, 1973.
[13] and B.A. LIFŠIC, The central limit theorem for stationary Markov processes, Soviet Math. Dokl. 19 (1978) 392-394. | Zbl | MR
[14] , On the central limit theorem and iterated logarithm law for stationary processes, Bull. Austral. Math. Soc. 12 (1975) 1-8. | Zbl | MR
[15] , A central limit theorem for a class of dependent random variables, Theory Probab. Appl. 8 (1963) 83-89. | Zbl | MR
[16] , Théorème de limite centrale pour une chaîne de Markov récurrente Harris positive, Annales Inst. H. Poincaré Probab. Statist. 14 (1978) 425-440. | Zbl | MR | Numdam
[17] and , Markov Chains and Stochastic Stability, Communications and Control Engineering Series, Springer, Berlin, 1993. | Zbl | MR
[18] , General Irreducible Markov Chains and Nonnegative Operators, Cambridge University Press, London, 1984. | Zbl | MR
[19] , Limit Theorems of Probability Theory: Sequences of Independent Random Variables, Oxford University Press, Oxford, 1995. | Zbl | MR
[20] , Covariance inequalities for strongly mixing processes, Annales Inst. H. Poincaré Probab. Statist. 29 (1993) 587-597. | Zbl | MR | Numdam
[21] , A maximal inequality and dependent Marcinkiewicz-Zygmund strong laws, Ann. Probab. 23 (1995) 918-937. | Zbl | MR
[22] , A central limit theorem and a strong mixing condition, Proc. Nat. Acad. Sci. USA 42 (1956) 43-47. | Zbl | MR
[23] and , Some limit theorem for random functions I, Theory Probab. Appl. 4 (1959) 178-197. | Zbl | MR
[24] and , Subgeometric rates of convergence of f -ergodic Markov chains, Adv. Appl. Probab. 26 (1994) 775-798. | Zbl | MR
[25] , Inequalities for absolutely regular sequences: application to density estimation, Probab. Theor. Related Fields 107 (1997) 467-492. | Zbl | MR
[26] , Approximating martingales and the central limit theorem for strictly stationary processes, Stoch. Processes Appl. 44 (1993) 41-74. | Zbl | MR






