Invariance principles for absolutely regular empirical processes
Annales de l'I.H.P. Probabilités et statistiques, Volume 31 (1995) no. 2, pp. 393-427.
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     author = {Doukhan, P. and Massart, P. and Rio, E.},
     title = {Invariance principles for absolutely regular empirical processes},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
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     url = {http://www.numdam.org/item/AIHPB_1995__31_2_393_0/}
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Doukhan, P.; Massart, P.; Rio, E. Invariance principles for absolutely regular empirical processes. Annales de l'I.H.P. Probabilités et statistiques, Volume 31 (1995) no. 2, pp. 393-427. http://www.numdam.org/item/AIHPB_1995__31_2_393_0/

N.T. Andersen, E. Giné, M. Ossiander and J. Zinn, The central limit theorem and the law of iterated logarithm for empirical processes under local conditions, Probab. Th. Rel. Fields, Vol. 77, 1988, pp. 271-305. | MR | Zbl

W.K. Andrews and D. Pollard, An introduction to functional central limit theorems for dependent stochastic processes, Inst. Stat. review, Vol. 62, 1994, pp. 119-132. | Zbl

M.A. Arcones and B. Yu, Central limit theorems for empirical and U-processes of stationary mixing sequences, J. Theoret. Prob., Vol. 7, 1994, pp. 47-71. | MR | Zbl

P. Bártfai, Über die Entfemung de Irrfahrtswege, Studia Sci. Math. Hungar, Vol. 1, 1970, pp. 161-168. | MR

R.F. Bass, Law of the iterated logarithm for set-indexed partial sum processes with finite variance, Z. Warsch. verw. Gebiete, Vol. 70, 1985, pp. 591-608. | MR | Zbl

H.C.P. Berbee, Random walks with stationary increments and renewal theory, Math. Cent. Tracts, Amsterdam, 1979. | MR | Zbl

I. Berkes and W. Phillip, An almost sure invariance principle for the empirical distribution of mixing random variables, Z. Wahrsch. Verw. Gebiete, Vol. 41, 1977, pp. 115-137. | MR | Zbl

E. Bolthausen, Weak convergence of an empirical process indexed by the closed convex subsets of I2, Z. Wahrsch. Verw. Gebiete, Vol. 43, 1978, pp. 173-181. | MR | Zbl

R.C. Bradley, Basic properties of strong mixing conditions, in Dependence in probability and statistics a survey of recent results, Oberwolfach 1985, Birkhäuser, 1986. | MR | Zbl

Yu. A. Davydov, Mixing conditions for Markov chains, Theory Probab. Appl., Vol. 28, 1973, pp. 313-328. | Zbl

S. Dhompongsa, A note on the almost sure approximation of empirical process of weakly dependent random vectors, Yokohama math. J., Vol. 32, 1984, pp. 113-121. | MR | Zbl

M. Donsker, Justification and extension of Doob's heuristic approach to the Kolmogorov-Smimov's theorems, Ann. Math. Stat., Vol. 23, 1952, pp. 277-281. | MR | Zbl

J.L. Doob, Stochastic Processes, Wiley, New-York, 1953. | MR | Zbl

P. Doukhan, Mixing: properties and examples, Lecture notes in Statistics 85, Springer, 1994. | MR | Zbl

P. Doukhan, J. León and F. Portal, Principe d'invariance faible pour la mesure empirique d'une suite de variables aléatoires dépendantes, Probab. Th. rel. fields, Vol. 76, 1987, pp. 51-70. | MR | Zbl

P. Doukhan, P. Massart and E. Rio, The functional central limit theorem for strongly mixing processes, Ann. Inst. H. Poincaré, Probab. Stat., Vol. 30, 1994, pp. 63-82. | Numdam | MR | Zbl

R.M. Dudley, Weak convergence of probabilities on nonseparable metric spaces and empirical measures on Euclidean spaces, Illinois J. Math., Vol. 10, 1966, pp. 109-126. | MR | Zbl

R.M. Dudley, The sizes of compact subsets of Hilbert space and continuity of Gaussian processes, J. Functional Analysis, Vol. 1, 1967, pp. 290-330. | MR | Zbl

R.M. Dudley, Central limit theorems for empirical measures, Ann. Probab., Vol. 6, 1978, pp. 899-929. | MR | Zbl

R.M. Dudley, A course on empirical processes. Ecole d'été de probabilités de Saint-Flour XII-1982. Lectures Notes in Math., Vol. 1097, Springer, Berlin, 1984, pp. 1-142. | MR | Zbl

M. Fréchet, Sur les tableaux de corrélation dont les marges sont données, Annales de l'université de Lyon, Sciences, section A, Vol. 14, 1951, pp. 53-77. | MR | Zbl

M. Fréchet, Sur la distance de deux lois de probabilité, C. R. Acad. Sci. Paris, Vol. 244, No. 6, 1957, pp. 689-692. | MR | Zbl

E. Giné and J. Zinn, Some limit theorems for empirical processes, Ann. Probab., Vol. 12, 1984, pp. 929-989. | MR | Zbl

N. Herrndorf, A functional central limit theorem for strongly mixing sequences of random variables, Z. Wahr. Verv. Gebiete, Vol. 69, 1985, pp. 541-550. | MR | Zbl

I.A. Ibragimov, Some limit theorems for stationary processes, Theory Probab. Appl., Vol. 7, 1962, pp. 349-382. | MR | Zbl

V.I. Kolchinskii, On the central limit theorem for empirical measures (In Russian), Teor. vero. i. mat. stat. (Kiev), Vol. 24, 1981, pp. 63-75. | MR | Zbl

A.N. Kolmogorov and Y.A. Rozanov, On the strong mixing conditions for stationary gaussian sequences, Theory Probab. Appl., Vol. 5, 1960, pp. 204-207. | Zbl

P. Massart, Invariance principles for empirical processes: the weakly dependent case, Quelques problèmes de vitesse de convergence pour des mesures empiriques. Thèse d'Etat, Université de Paris-Sud, 1987.

A. Mokkadem, Propriétés de mélange des modèles autorégressifs polynomiaux, Ann. Inst. Henri Poincaré, Probab. Stat., Vol. 26, 1990, pp. 219-260. | Numdam | MR | Zbl

M. Ossiander, A central limit theorem under metric entropy with L2-bracketing, Ann. Probab., Vol. 15, 1987, pp. 897-919. | MR | Zbl

W. Philipp and L. Pinzur, Almost sure approximation theorems for the multivariate empirical processes, Z. Wahr. Verv. Gebiete, Ser. A, Vol. 54, 1980, pp. 1-13. | MR | Zbl

D. Pollard, A central limit theorems for empirical processes, J. Aust. Math. Soc., Vol. 33, 1982, pp. 235-248. | MR | Zbl

D. Pollard, Convergence of stochastic processes, Springer, Berlin, 1984. | MR | Zbl

D. Pollard, Empirical processes: theory and applications, NSF-CBMS Regional Conference Series in Probability and Statistics IMS-ASA, Hayward-Alexandria, 1990. | MR | Zbl

P. Révész, Three theorems of multivariate empirical process. Lectures Notes in Math., Vol. 566, Springer, Berlin, 1976, pp. 106-126. | MR | Zbl

E. Rio, Covariance inequalities for strongly mixing processes, Ann. Int. H. Poincaré, Prob. Stat., Vol. 29, 1993, pp. 587-597. | Numdam | MR | Zbl

M. Rosenblatt, A central limit theorem and a strong mixing condition, Proc. Nat. Ac. Sc. U.S.A., Vol. 42, 1956, pp. 43-47. | MR | Zbl

A.V. Skorohod, On a representation of random variables, Theory Probab. Appl., Vol. 21, 1976, pp. 628-632. | MR | Zbl

T.G. Sun, Ph. D. dissertation, Dept of Mathematics, Univ. of Washington, Seattle, 1976.

M. Talagrand, Regularity of Gaussian processes, Acta Math., Vol. 159, 1987, pp. 99-149. | MR | Zbl

V.A. Volkonskii and Y.A. Rozanov, Some limit theorems for random functions, Part I, Theory Probab. Appl., Vol. 4, 1959, pp. 178-197. | MR | Zbl

K. Yoshihara, Note on an almost sure invariance principle for some empirical processes, Yokohama math. J., Vol. 27, 1979, pp. 105-110. | MR | Zbl