Geodesic
Improved multivariate version of the second Kolmogorov's uniform limit theorem
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 28, Tome 486 (2019), pp. 71-85
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The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent summands by the infinitely divisible laws may be transferred to the estimation of the closeness of distributions on convex polyhedra. 
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F. Götze; A. Yu. Zaitsev; D. Zaporozhets. Improved multivariate version of the second Kolmogorov's uniform limit theorem. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 28, Tome 486 (2019), pp. 71-85. http://geodesic.mathdoc.fr/item/ZNSL_2019_486_a4/

[1] T. V. Arak, A. Yu. Zaitsev, Ravnomernye predelnye teoremy dlya summ nezavisimykh sluchainykh velichin, Tr. MIAN SSSR, 174, 1986, 214 pp.

[2] A. A. Borovkov, A. I. Sakhanenko, “Ob otsenkakh skorosti skhodimosti v printsipe invariantnosti dlya banakhovykh prostranstv”, Teoriya veroyatn. i ee primen., 25:4 (1980), 734–744 | MR | Zbl

[3] F. Gettse, A. Yu. Zaitsev, “Otsenki blizosti svertok veroyatnostnykh raspredelenii na vypuklykh mnogogrannikakh”, Zap. nauchn. semin. POMI, 474, 2018, 108–117 | MR

[4] I. A. Ibragimov, E. L. Presman, “O skorosti sblizheniya raspredelenii summ nezavisimykh sluchainykh velichin s soprovozhdayuschimi zakonami”, Teoriya veroyatn. i ee primen., 18:4 (1973), 753–766 | MR | Zbl

[5] A. N. Kolmogorov, “Dve ravnomernye predelnye teoremy dlya summ nezavisimykh slagaemykh”, Teoriya veroyatn. i ee primen., 1:4 (1956), 384–394

[6] A. N. Kolmogorov, “O priblizhenii raspredelenii summ nezavisimykh slagaemykh neogranichenno delimymi raspredeleniyami”, Trudy Moskov. matem. ob-va, 12, 1963, 437–451

[7] L. Le Cam, “On the distribution of sums of independent random variables”, Bernoulli, Bayes, Laplace (anniversary volume), Springer, Berlin–Heidelberg–N.Y., 1965, 179–202 | MR

[8] B. A. Rogozin, “Ob odnoi otsenke funktsii kontsentratsii”, Teoriya veroyatn. i ee primen., 6:1 (1961), 103–105

[9] B. A. Rogozin, “Ob uvelichenii rasseivaniya summ nezavisimykh sluchainykh velichin”, Teoriya veroyatn. i ee primen., 6:1 (1961), 106–108

[10] A. Yu. Zaitsev, “Neskolko zamechanii ob approksimatsii raspredelenii summ nezavisimykh slagaemykh”, Zap. nauchn. semin. LOMI, 136, 1984, 48–57

[11] A. Yu. Zaitsev, “Mnogomernyi variant vtoroi ravnomernoi predelnoi teoremy Kolmogorova”, Teoriya veroyatn. i ee primen., 34:1 (1989), 128–151 | MR

[12] A. Yu. Zaitsev, “Ob odnom klasse neravnomernykh otsenok v mnogomernykh predelnykh teoremakhs”, Zap. nauchn. sem. POMI, 184, 1990, 92–105

[13] A. Yu. Zaitsev, T. V. Arak, “O skorosti skhodimosti vo vtoroi ravnomernoi predelnoi teoreme Kolmogorova”, Teoriya veroyatn. i ee primen., 28:2 (1984), 333–353