@article{AIHPB_1989__25_4_429_0,
author = {Rachev, S. T. and Yukich, J. E.},
title = {Smoothing metrics for measures on groups},
journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
pages = {429--441},
year = {1989},
publisher = {Gauthier-Villars},
volume = {25},
number = {4},
mrnumber = {1045244},
zbl = {0698.60007},
language = {en},
url = {https://www.numdam.org/item/AIHPB_1989__25_4_429_0/}
}
TY - JOUR AU - Rachev, S. T. AU - Yukich, J. E. TI - Smoothing metrics for measures on groups JO - Annales de l'I.H.P. Probabilités et statistiques PY - 1989 SP - 429 EP - 441 VL - 25 IS - 4 PB - Gauthier-Villars UR - https://www.numdam.org/item/AIHPB_1989__25_4_429_0/ LA - en ID - AIHPB_1989__25_4_429_0 ER -
Rachev, S. T.; Yukich, J. E. Smoothing metrics for measures on groups. Annales de l'I.H.P. Probabilités et statistiques, Tome 25 (1989) no. 4, pp. 429-441. https://www.numdam.org/item/AIHPB_1989__25_4_429_0/
[A1] , Probability Inequalities for Empirical Processes and a Law of the Iterated Logarithm, Ann. Prob., Vol. 12, 1984, pp. 1041-1067; Correction, Vol. 15, 1987, pp. 428-430. | Zbl | MR
[BF] and , Potential Theory on Locally Compact Abelian Groups, Springer-Verlag, 1975. | Zbl | MR
[DDF] , and , On Merging of Probabilities, Technical Report No. 301, 1988, Dept of Statistics, Stanford, California. | Zbl
[Du1] , Convergence of Baire Measures, Studia Mathematica, Vol. XXVII, 1966, pp. 251-268. | Zbl | MR
[Du2] , Probabilities and Metrics, Aarhus Universitet Lecture Notes Series, No. 45, 1976. | Zbl | MR
[Du3] , Universal Donsker Classes and Metric Entropy, Ann. Prob., Vol. 15, 1987, pp. 1306-1326. | Zbl | MR
[DP] and , Invariance Principles for Sums of Banach Space Valued Random Elements and Empirical Processes, Z. Wahr. v. Geb., Vol. 62, 1983, pp. 509-552. | Zbl | MR
[Fe] , An Introduction to Probability Theory and its Applications, Vol. 2, 1971, second edition, Wiley and Sons. | Zbl | MR
[GZ1] and , Some Limit Theorems for Empirical Processes, Ann. Prob., Vol. 12, 1984, pp. 929-989. | Zbl | MR
[GZ2] and , Lecture on the Central Limit Theorem for Empirical Processes, Lecture Notes in Mathematics, No. 1221, 1985, Springer, pp. 50-113. | Zbl | MR
[HR] and , Abstract Harmonic Analysis, Vol. I, 1979, Springer-Verlag. | Zbl | MR
[KM] and , Gleichverteilungseigenschaften von Faltungen von Verteilungsgesetzen auf lokalkompakten abelschen Gruppen, I., Math. Nachr., Vol. 37, 1968, pp. 267-312. | Zbl | MR
[Ko] , Some Recent Work in the Field of Limit Theorems in Probability Theory, Moscow Vestnik, Vol. 10, 1953, pp. 29-38. | Zbl
[Ma] , Rates of Convergence in the Central Limit Theorem for Empirical Processes, Lecture Notes Math., No. 1193, 1986, pp. 73-109. | MR
[Po] , Convergence of Stochastic Processes, Springer-Verlag, 1984. | Zbl | MR
[Ra] , Minimal Metrics in a Space of Real-Valued Random Variables, Soviet Math. Dokl., Vol. 23/2, 1981, pp. 425-428. | Zbl
[RI] , and , Ideal Quadratic Metrics, Stability Problems of Stochastic Models, Seminar Proceedings, V.N.I.I.S.I., Moscow), pp. 119-128 (Russian); J. Soviet Math, Vol. 35, No. 2, 1986, pp. 2386-2394 (English). | Zbl | MR
[RY] and , Rates for the CLT via New Ideal Metrics, Ann. Prob., Vol. 17, 1989, pp. 775-788. | Zbl | MR
[Ru1] , Fourier Analysis on Groups, Interscience Publishers, 1962. | Zbl | MR
[Ru2] , Personal communication, August 1986.
[Se] , On Some Properties of Metrics on the Set of Distribution Functions, Math. U.S.S.R. Sbornik, Vol. 31, No. 3, 1977, pp. 379-387. | Zbl
[Si] , Convergence and Convolutions of Probability Measures on a Topological Group, Ann. Prob., Vol. 4, 1976, pp. 433-443. | Zbl | MR
[St] , The Existence of Probability Measures with Given Marginals, Ann. Math. Statist., Vol. 36, 1965, pp. 423-439. | Zbl | MR
[Sz] , On a Metrization of the Vague Convergence, Stud. Sci. Math. Hungar., Vol. 9, 1974, pp. 219-222. | Zbl | MR
[Va] , Measures on Topological Spaces (in Russian), Mathematicheskii Sbornik, Vol. 55, (97), 1961, pp. 35-100. | Zbl | MR
[Yu1] , The Convolution Metric dg, Math. Proc. Camb. Phil. Soc., Vol. 98, 1985, pp. 533-540. | Zbl | MR
[Yu2] , Uniform Exponential Bounds for the Normalized Empirical Process, Studia Mathematica, Vol. 84, No. 2, 1986, pp. 71-78. | Zbl | MR
[Zo] , Probability Metrics, Theory Prob. Appl., Vol. 28, (2), 1986, pp. 278-302. | Zbl | MR






