Approximation forte de processus de sommes partielles indexés par des ensembles
Thèses d'Orsay, no. 275 (1990) , 126 p. 
@phdthesis{BJHTUP11_1990__0275__P0_0,
     author = {Rio, Emmanuel},
     title = {Approximation forte de processus de sommes partielles index\'es par des ensembles},
     series = {Th\`eses d'Orsay},
     year = {1990},
     publisher = {Universit\'e de Paris-Sud Centre d'Orsay},
     number = {275},
     language = {fr},
     url = {https://www.numdam.org/item/BJHTUP11_1990__0275__P0_0/}
}
TY  - BOOK
AU  - Rio, Emmanuel
TI  - Approximation forte de processus de sommes partielles indexés par des ensembles
T3  - Thèses d'Orsay
PY  - 1990
IS  - 275
PB  - Université de Paris-Sud Centre d'Orsay
UR  - https://www.numdam.org/item/BJHTUP11_1990__0275__P0_0/
LA  - fr
ID  - BJHTUP11_1990__0275__P0_0
ER  - 
%0 Book
%A Rio, Emmanuel
%T Approximation forte de processus de sommes partielles indexés par des ensembles
%S Thèses d'Orsay
%D 1990
%N 275
%I Université de Paris-Sud Centre d'Orsay
%U https://www.numdam.org/item/BJHTUP11_1990__0275__P0_0/
%G fr
%F BJHTUP11_1990__0275__P0_0
Rio, Emmanuel. Approximation forte de processus de sommes partielles indexés par des ensembles. Thèses d'Orsay, no. 275 (1990), 126 p. https://www.numdam.org/item/BJHTUP11_1990__0275__P0_0/

Alexander, K.S. (1987). Central limit theorems for stochastic processes under random entropy conditions. Probab. Theory Related Fields 75 351-378. | MR | Zbl

Alexander, K.S. and Pyke, R. (1986). A uniform central limit theorem for set-indexed partial-sum processes with finite variance. Ann. Probab. 14 582-597. | MR | Zbl

Bass, R.F. (1985). Law of the iterated logarithm for partial-sum processes with finite variance. Z. Wahrsch. verw. Gebiete 70 591-608. | MR | Zbl | DOI

Bass, R.F. and Pyke, R. (1984). Functional law of the iterated logarithm and uniform central limit theorem for partial-sum processes indexed by sets. Ann. Probab. 12 13-34. | MR | Zbl

Beck, J. (1985). Lower bounds on the approximation of the multivariate empirical process. Z. Wahrsch. verw. Gebiete 70 289-306. | MR | Zbl | DOI

Beck, J. (1987). Irregularities of distribution I. Acta Math. 159 1-49. | MR | Zbl

Breiman, L. (1967). On the tail behavior of sums of independent random variables. Z. Wahrsch. verw. Gebiete 9 20-25. | MR | Zbl | DOI

Csörgó, M. and Révész, P. (1981). Strong Approximations in Probabilities and Statistics. Academic, New York. | MR | Zbl

Dudley, R.M. (1973). Sample functions of the Gaussian process. Ann. Probab. 1 66-103. | MR | Zbl

Dudley, R.M. (1974). Metric entropy of some classes of sets with differentiable boundaries. J. Approx. Theory 10 227-236. | MR | Zbl | DOI

Dudley, R.M. (1978). Central limit theorems for empirical measures. Ann. Probab. 7 899-929. | MR | Zbl

Einmahl, U. (1987). Strong invariance principle for partial sums of independent random vectors. Ann. Probab. 15 1419-1440. | MR | Zbl

Einmahl, U. (1989). Extensions of results of Komlós, Major and Tusnády to the multivariate case. J. Multivariate Analysis 28 20-68. | MR | Zbl | DOI

Einmahl, U. (1989). The Darling-Erdös Theorem for Sums of I.I.D. Random Variables. Probab. Th. Rel. Fields. 82 241-247. | MR | Zbl

Hanson, D. L. and Russo, R. P. (1983). Some Results on the Wiener Process with Applications to LAG Sums of I.I.D. Random Variables. Ann. Probab. 11 609-623. | MR | Zbl

Hanson, D. L. and Russo, R. P. (1989). Some Liminf Results for Increments of a Wiener Process. Ann. Probab. 17 1063-1082. | MR | Zbl

Komlós, J., Major, P. and Tusnády, G. (1975). An approximation of partial sums of independent rv's and the sample df. I. Z. Wahrsch. verw. Gebiete 32 111-6131. | MR | Zbl | DOI

Komlós, J., Major, P. and Tusnády, G. (1976). An approximation of partial sums of independent rv's and the sample df. II. Z. Wahrsch. verw. Gebiete 34 35-58. | MR | Zbl | DOI

Major, P. (1976). Approximation of partial sums of i.i.d.r.v.'s when the summands have only two moments. Z. Wahrsch. verw. Gebiete 35 221-229. | MR | Zbl | DOI

Massart, P. (1989). Strong approximation for multivariate empirical and related processese, via K.M.T. constructions. Ann. Probab. 17 266-291. | MR | Zbl

Massart, P. (1987). Quelques problèmes de vitesse de convergence pour des processus empiriques. Thèse de doctorat d'Etat, Université de Paris-Sud, Orsay.

Morrow, E.J. and Philipp, W. (1986). Invariance principles for partial sum processes and empirical processes indexed by sets. Probab. Theory Related Fields 73 11-42. | MR | Zbl

Pyke, R. (1984). Asymptotic results for empirical and partial-sum processes : A review. Canad. J. Statist. 12 241-264. | MR | Zbl | DOI

Sakhanenko, A.I. (1984). Rate of convergence in the invariance principle for variables with exponential moments that are not identically distributed. In Limit Theorems for Sums of Random Variables 4-49. Trudy Inst. Mat. Vol. 3, "Nauka" Sibirsk.Otdel, Novosibirsk [Russian]. | MR

Shao, Q-M. (1989). On a Problem of Csörgó et Révész. Ann. of Probab. 17 809-812. | MR | Zbl

Strassen, V. (1964). An invariance principle for the law of the iterated logarithm. Z. Wahrsch. Verw. Geb. 3 211-226. | MR | Zbl | DOI

Tusnády, G. (1978). A remark on the approximation of the sample DF in the multidimensional case. Period. Math. Hung. 8. 53-55. | MR | Zbl

Alexander, K.S. (1987). Central limit theorems for stochastic processes under random entropy conditions. Probab. Theory Related Fields 75 351-378. | MR | Zbl

Alexander, K.S. and Pyke, R. (1986). A uniform central limit theorem for set-indexed partial-sum processes with finite variance. Ann. Probab. 14 582-597. | MR | Zbl

Assouad, P. (1983). Densité et dimension. Ann. Inst. Fourier (Grenoble) 33 (3) 233-282. | MR | Zbl | Numdam

Bass, R.F. (1985). Law of the iterated logarithm for partial-sum processes with finite variance. Z. Wahrsch. verw. Gebiete 70 591-608. | MR | Zbl | DOI

Bass, R.F. and Pyke, R. (1984). Functional law of the iterated logarithm and uniform central limit theorem for partial-sum processes indexed by sets. Ann. Probab. 12 13-34. | MR | Zbl

Beck, J. (1985). Lower bounds on the approximation of the multivariate empirical process. Z. Wahrsch. verw. Gebiete 70 289-306. | MR | Zbl | DOI

Breiman, L. (1967). On the tail behavior of sums of independent random variables. Z. Wahrsch. verw. Gebiete 9 20-25. | MR | Zbl | DOI

Csörgó, M. and Révész, P. (1981). Strong Approximations in Probabilities and Statistics. Academic, New York. | MR | Zbl

Dudley, R.M. (1978). Central limit theorems for empirical measures. Ann. Probab. 7 899-929. | MR | Zbl

Einmahl, U. (1987). Strong invariance principle for partial sums of independent random vectors. Ann. Probab. 15 1419-1440. | MR | Zbl

Einmahl, U. (1989). Extensions of results of Komlós, Major and Tusnády to the multivariate case. J. Multivariate Analysis 28 20-68. | MR | Zbl | DOI

Komlós, J., Major, P. and Tusnády, G. (1975). An approximation of partial sums of independent rv's and the sample df. I. Z. Wahrsch. verw. Gebiete 32 111-6131. | MR | Zbl | DOI

Komlós, J., Major, P. and Tusnády, G. (1976). An approximation of partial sums of independent rv's and the sample df. II. Z. Wahrsch. verw. Gebiete 34 35-58. | MR | Zbl | DOI

Major, P. (1976). Approximation of partial sums of i.i.d.r.v.'s when the summands have only two moments. Z. Wahrsch. verw. Gebiete 35 221-229. | MR | Zbl | DOI

Major, P. (1978). On the Invariance Principle for Sums of Independent Identically Distributed Random Variables. J. Multivariate Analysis 8 487-517. | MR | Zbl | DOI

Massart, P. (1989). Strong approximation for multivariate empirical and related processese, via K.M.T. constructions. Ann. Probab. 17 266-291. | MR | Zbl

Massart, P. (1987). Quelques problèmes de vitesse de convergence pour des processus empiriques. Thèse de doctorat d'Etat, Université de Paris-Sud, Orsay.

Morrow, E.J. and Philipp, W. (1986). Invariance principles for partial sum processes and empirical processes indexed by sets. Probab. Theory Related Fields 73 11-42. | MR | Zbl

Philipp, W. (1980). Weak and L p -invariance principles for sums of B -valued random variables. Ann. Probab. 8 68-82. | MR | Zbl

Pollard, D. (1984). Convergence of Stochastic Processes. Springer Series in Statistics. | MR | Zbl | DOI

Pyke, R. (1984). Asymptotic results for empirical and partial-sum processes : A review. Canad. J. Statist. 12 241-264. | MR | Zbl | DOI

Sakhanenko, A.I. (1984). Rate of convergence in the invariance principle for variables with exponential moments that are not identically distributed. In Limit Theorems for Sums of Random Variables 4-49. Trudy Inst. Mat. Vol. 3, "Nauka" Sibirsk.Otdel, Novosibirsk [Russian]. | MR

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

Strassen, V. (1964). An invariance principle for the law of the iterated logarithm. Z. Wahrsch. Verw. Geb. 3 211-226. | MR | Zbl | DOI

Zolotarev, V.M. (1983). Probability metrics. Theory Probab. Appl. 28 278-302. | Zbl

Alexander, K.S. and Pyke, R. (1986). A uniform central limit theorem for set-indexed partial-sum processes with finite variance. Ann. Probab. 14 582-597. | MR | Zbl

Bass, R.F. (1985). Law of the iterated logarithm for partial-sum processes with finite variance. Z. Wahrsch. verw. Gebiete 70 591-608. | MR | Zbl | DOI

Bass, R.F. and Pyke, R. (1984). Functional law of the iterated logarithm and uniform central limit theorem for partial-sum processes indexed by sets. Ann. Probab. 12 13-34. | MR | Zbl

Beck, J. (1985). Lower bounds on the approximation of the multivariate empirical process. Z. Wahrsch. verw. Gebiete 70 289-306. | MR | Zbl | DOI

Beck, J. (1987). Irregularities of distribution I. Acta Math. 159 1-49. | MR | Zbl

Borisov, I.S. (1985). Upper and lower estimates of the convergence rate in the invariance principle. Proceedings of the fourth Vilnius conference I, VNU Science Press. 251-259. | MR | Zbl

Breiman, L. (1967). On the tail behavior of sums of independent random variables. Z. Wahrsch. verw. Gebiete 9 20-25. | MR | Zbl | DOI

Dudley, R.M. (1973). Sample functions of the Gaussian process. Ann. Probab. 1 66-103. | MR | Zbl

Dudley, R.M. (1974). Metric entropy of some classes of sets with differentiable boundaries. J. Approx. Theory 10 227-236. | MR | Zbl | DOI

Dudley, R.M. (1978). Central limit theorems for empirical measures. Ann. Probab. 7 899-929. | MR | Zbl

Einmahl, U. (1987). Strong invariance principle for partial sums of independent random vectors. Ann. Probab. 15 1419-1440. | MR | Zbl

Einmahl, U. (1989). Extensions of results of Komlós, Major and Tusnády to the multivariate case. J. Multivariate Analysis 28 20-68. | MR | Zbl | DOI

Komlós, J., Major, P. and Tusnády, G. (1975). An approximation of partial sums of independent rv's and the sample df. I. Z. Wahrsch. verw. Gebiete 32 111-6131. | MR | Zbl | DOI

Komlós, J., Major, P. and Tusnády, G. (1976). An approximation of partial sums of independent rv's and the sample df. II. Z. Wahrsch. verw. Gebiete 34 35-58. | MR | Zbl | DOI

Major, P. (1976). Approximation of partial sums of i.i.d.r.v.'s when the summands have only two moments. Z. Wahrsch. verw. Gebiete 35 221-229. | MR | Zbl | DOI

Major, P. (1978). On the Invariance Principle for Sums of Independent Identically Distributed Random Variables. J. Multivariate Analysis 8 487-517. | MR | Zbl | DOI

Massart, P. (1989). Strong approximation for multivariate empirical and related processese, via K.M.T. constructions. Ann. Probab. 17 266-291. | MR | Zbl

Massart, P. (1989). About the constant in the DKW inequality. To appear in Ann. of Probab.

Massart, P. (1987). Quelques problèmes de vitesse de convergence pour des processus empiriques. Thèse de doctorat d'Etat, Université de Paris-Sud, Orsay.

Meyer, P.A. (1972). Martingales and stochastics intégrais I. Lecture Notes in Mathematics 284. | MR | Zbl

Morrow, E.J. and Philipp, W. (1986). Invariance principles for partial sum processes and empirical processes indexed by sets. Probab. Theory Related Fields 73 11-42. | MR | Zbl

Philipp, W. (1980). Weak and L p -invariance principles for sums of B -valued random variables. Ann. Probab. 8 68-82. | MR | Zbl

Pollard, D. (1984). Convergence of Stochastic Processes. Springer Series in Statistics. | MR | Zbl | DOI

Pyke, R. (1984). Asymptotic results for empirical and partial-sum processes : A review. Canad. J. Statist. 12 241-264. | MR | Zbl | DOI

Sakhanenko, A.I. (1984). Rate of convergence in the invariance principle for variables with exponential moments that are not identically distributed. In Limit Theorems for Sums of Random Variables 4-49. Trudy Lost. Mat. Vol. 3, "Nauka" Sibirsk. Otdel, Novosibirsk [Russian]. | MR

Beck, J. (1985). Lower bounds on the approximation of the multivariate empirical process. Z. Wahrsch. verw. Gebiete 70 289-306. | MR | Zbl | DOI

Bennett, G. (1962). Probability inequalities for sums of independent random variables. J. Amer. Statist. Assoc. 57 33-45. | Zbl | DOI

Breiman, L. (1967). On the tail behavior of sums of independent random variables. Z. Wahrsch. verw. Gebiete 9 20-25. | MR | Zbl | DOI

Einmahl, U. (1987). Strong invariance principle for partial sums of independent random vectors. Ann. Probab. 15 1419-1440. | MR | Zbl

Einmahl, U. (1989). Extensions of results of Komlós, Major and Tusnády to the multivariate case. J. Multivariate Analysis 28 20-68. | MR | Zbl | DOI

Komlós, J., Major, P. and Tusnády, G. (1975). An approximation of partial sums of independent rv's and the sample df. I. Z. Wahrsch. verw. Gebiete 32 111-6131. | MR | Zbl | DOI

Komlós, J., Major, P. and Tusnády, G. (1976). An approximation of partial sums of independent rv's and the sample df. II. Z. Wahrsch. verw. Gebiete 34 35-58. | MR | Zbl | DOI

Major, P. (1976). Approximation of partial sums of i.i.d.r.v.'s when the summands have only two moments. Z. Wahrsch. verw. Gebiete 35 221-229. | MR | Zbl | DOI

Massart, P. (1989). Strong approximation for multivariate empirical and related processese, via K.M.T. constructions. Ann. Probab. 17 266-291. | MR | Zbl

Massart, P. (1987). Quelques problèmes de vitesse de convergence pour des processus empiriques. Thèse de doctorat d'Etat, Université de Paris-Sud, Orsay.

Sakhanenko, A.I. (1984). Rate of convergence in the invariance principle for variables with exponential moments that are not identically distributed. In Limit Theorems for Sums of Random Variables 4-49. Trudy Inst. Mat. Vol. 3, "Nauka" Sibirsk.Otdel, Novosibirsk [Russian]. | MR

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

Tusnády, G. (1978). A remark on the approximation of the sample DF in the multidimensional case. Period. Math. Hung. 8. 53-55. | MR | Zbl

Wichura, M.J. (1973). Some Strassen type laws of the iterated logarithm for multiparameter stochastic processes. Ann. Probab. 1. 272-296. | MR | Zbl