Smoothing metrics for measures on groups
Annales de l'I.H.P. Probabilités et statistiques, Volume 25 (1989) no. 4, p. 429-441
@article{AIHPB_1989__25_4_429_0,
     author = {Rachev, S. T. and Yukich, Joseph E.},
     title = {Smoothing metrics for measures on groups},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {25},
     number = {4},
     year = {1989},
     pages = {429-441},
     zbl = {0698.60007},
     mrnumber = {1045244},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1989__25_4_429_0}
}
Rachev, S. T.; Yukich, J. E. Smoothing metrics for measures on groups. Annales de l'I.H.P. Probabilités et statistiques, Volume 25 (1989) no. 4, pp. 429-441. http://www.numdam.org/item/AIHPB_1989__25_4_429_0/

[A1] K.S. Alexander, 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. | MR 757769 | Zbl 0549.60024

[BF] C. Berg and G. Forst, Potential Theory on Locally Compact Abelian Groups, Springer-Verlag, 1975. | MR 481057 | Zbl 0308.31001

[DDF] A. D'Aristotile, P. Diaconis and D. Freedman, On Merging of Probabilities, Technical Report No. 301, 1988, Dept of Statistics, Stanford, California. | Zbl 0698.60005

[Du1] R.M. Dudley, Convergence of Baire Measures, Studia Mathematica, Vol. XXVII, 1966, pp. 251-268. | MR 200710 | Zbl 0147.31301

[Du2] R.M. Dudley, Probabilities and Metrics, Aarhus Universitet Lecture Notes Series, No. 45, 1976. | MR 488202 | Zbl 0355.60004

[Du3] R.M. Dudley, Universal Donsker Classes and Metric Entropy, Ann. Prob., Vol. 15, 1987, pp. 1306-1326. | MR 905333 | Zbl 0631.60004

[DP] R.M. Dudley and W. Philipp, Invariance Principles for Sums of Banach Space Valued Random Elements and Empirical Processes, Z. Wahr. v. Geb., Vol. 62, 1983, pp. 509-552. | MR 690575 | Zbl 0488.60044

[Fe] W. Feller, An Introduction to Probability Theory and its Applications, Vol. 2, 1971, second edition, Wiley and Sons. | MR 270403 | Zbl 0219.60003

[GZ1] E. Giné and J. Zinn, Some Limit Theorems for Empirical Processes, Ann. Prob., Vol. 12, 1984, pp. 929-989. | MR 757767 | Zbl 0553.60037

[GZ2] E. Giné and J. Zinn, Lecture on the Central Limit Theorem for Empirical Processes, Lecture Notes in Mathematics, No. 1221, 1985, Springer, pp. 50-113. | MR 875007 | Zbl 0605.60026

[HR] E. Hewitt and K.A. Ross, Abstract Harmonic Analysis, Vol. I, 1979, Springer-Verlag. | MR 551496 | Zbl 0416.43001

[KM] J. Kerstan and K. Matthes, Gleichverteilungseigenschaften von Faltungen von Verteilungsgesetzen auf lokalkompakten abelschen Gruppen, I., Math. Nachr., Vol. 37, 1968, pp. 267-312. | MR 242206 | Zbl 0214.43603

[Ko] A.N. Kolmogorov, Some Recent Work in the Field of Limit Theorems in Probability Theory, Moscow Vestnik, Vol. 10, 1953, pp. 29-38. | Zbl 0052.36202

[Ma] P. Massart, Rates of Convergence in the Central Limit Theorem for Empirical Processes, Lecture Notes Math., No. 1193, 1986, pp. 73-109. | MR 855853 | Zbl 0615.60032

[Po] D. Pollard, Convergence of Stochastic Processes, Springer-Verlag, 1984. | MR 762984 | Zbl 0544.60045

[Ra] S.T. Rachev, Minimal Metrics in a Space of Real-Valued Random Variables, Soviet Math. Dokl., Vol. 23/2, 1981, pp. 425-428. | Zbl 0473.60025

[RI] S.T. Rachev, and Ts.G. Ignatov, 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). | MR 859218 | Zbl 0596.60017

[RY] S.T. Rachev and J.E. Yukich, Rates for the CLT via New Ideal Metrics, Ann. Prob., Vol. 17, 1989, pp. 775-788. | MR 985389 | Zbl 0675.60018

[Ru1] W. Rudin, Fourier Analysis on Groups, Interscience Publishers, 1962. | MR 152834 | Zbl 0107.09603

[Ru2] W. Rudin, Personal communication, August 1986.

[Se] V.V. Senatov, 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 0387.60023

[Si] E. Siebert, Convergence and Convolutions of Probability Measures on a Topological Group, Ann. Prob., Vol. 4, 1976, pp. 433-443. | MR 413217 | Zbl 0338.60012

[St] V. Strassen, The Existence of Probability Measures with Given Marginals, Ann. Math. Statist., Vol. 36, 1965, pp. 423-439. | MR 177430 | Zbl 0135.18701

[Sz] D. Szasz, On a Metrization of the Vague Convergence, Stud. Sci. Math. Hungar., Vol. 9, 1974, pp. 219-222. | MR 391209 | Zbl 0325.60008

[Va] V.S. Varadarajan, Measures on Topological Spaces (in Russian), Mathematicheskii Sbornik, Vol. 55, (97), 1961, pp. 35-100. | MR 148838 | Zbl 0152.04202

[Yu1] J.E. Yukich, The Convolution Metric dg, Math. Proc. Camb. Phil. Soc., Vol. 98, 1985, pp. 533-540. | MR 803612 | Zbl 0576.60006

[Yu2] J.E. Yukich, Uniform Exponential Bounds for the Normalized Empirical Process, Studia Mathematica, Vol. 84, No. 2, 1986, pp. 71-78. | MR 871846 | Zbl 0624.60047

[Zo] V.M. Zolotarev, Probability Metrics, Theory Prob. Appl., Vol. 28, (2), 1986, pp. 278-302. | MR 700210 | Zbl 0533.60025