Abstract:
In the paper, by the method of characteristic functions, an estimate of the convergence rate in the multi-dimensional central limit theorem is obtained. The estimate is non-uniform; it depends on the location with respect to the origin of the set the measures of which are compaired.
Citation:
V. I. Rotar', “A nonuniform estimate of the speed of convergence in the multidimensional central limit theorem”, Teor. Veroyatnost. i Primenen., 15:4 (1970), 647–665; Theory Probab. Appl., 15:4 (1970), 630–648
\Bibitem{Rot70}
\by V.~I.~Rotar'
\paper A~nonuniform estimate of the speed of convergence in the multidimensional central limit theorem
\jour Teor. Veroyatnost. i Primenen.
\yr 1970
\vol 15
\issue 4
\pages 647--665
\mathnet{http://mi.mathnet.ru/tvp1932}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=283858}
\zmath{https://zbmath.org/?q=an:0235.60026}
\transl
\jour Theory Probab. Appl.
\yr 1970
\vol 15
\issue 4
\pages 630--648
\crossref{https://doi.org/10.1137/1115072}
Linking options:
https://www.mathnet.ru/eng/tvp1932
https://www.mathnet.ru/eng/tvp/v15/i4/p647
This publication is cited in the following 25 articles:
N. G. Gamkrelidze, “Issledovaniya po reshetchatym raspredeleniyam teorii veroyatnostei”, Issledovaniya po reshetchatym raspredeleniyam teorii veroyatnostei, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 218, VINITI RAN, M., 2022, 3–66
Theory Probab. Appl., 52:4 (2008), 636–650
Bogatyrev S.A., Goetze F., Ulyanov V.V., “Non–uniform bounds for short asymptotic expansions in the CLT for balls in a Hilbert space”, Journal of Multivariate Analysis, 97:9 (2006), 2041–2056
Françoise Pène, “Rate of convergence in the multidimensional central limit theorem for stationary processes. Application to the Knudsen gas and to the Sinai billiard”, Ann. Appl. Probab., 15:4 (2005)
Françoise Pène, “Multiple decorrelation and rate of convergence in multidimensional limit theorems for the Prokhorov metric”, Ann. Probab., 32:3B (2004)
P. G. Grigor'ev, “Random Linear Combinations of Functions from L1”, Math. Notes, 74:2 (2003), 185–211
V. A. Koval', “The Law of the Iterated Logarithm for Matrix-Normed Sums of Independent Random Variables and Its Applications”, Math. Notes, 72:3 (2002), 331–336
S. A. Bogatyrev, “A nonuniform estimate for the error in short asymptotic expansions in Hilbert space”, Theory Probab. Appl., 47:4 (2003), 689–692
L. V. Kiryanova, V. I. Rotar, “A lemma on «corrected» distributions”, Theory Probab. Appl., 31:4 (1987), 708–712
A. V. Asriev, V. I. Rotar', “On the rate of convergence in the infinite-dimensional central limit theorem for the probability of hitting a parallelepiped”, Theory Probab. Appl., 30:4 (1986), 691–701
L. V. Osipov, V. I. Rotar', “On an infinite-dimensional central limit theorem”, Theory Probab. Appl., 29:2 (1985), 375–383
N. G. Gamkrelidze, “On the estimate of the distance in variance between the distributions”, Theory Probab. Appl., 28:2 (1984), 467–469
A. K. Aleškevičiene, “Multidimensional integral limit theorems for large deviations”, Theory Probab. Appl., 28:1 (1984), 65–88
V. I. Rotar', “On summation of independent variables in a non-classical situation”, Russian Math. Surveys, 37:6 (1982), 151–175
V. V. Yurinskiǐ, “On the accuracy of Gaussian approximation for the probability of hitting a ball”, Theory Probab. Appl., 27:2 (1983), 280–289
S. V. Fomin, “Estimates of the rate of convergence in the multidimensional central limit theorem”, Theory Probab. Appl., 27:2 (1983), 365–368
R. M. Gil'fanov, “A nonuniform estimate of the rate of convergence in the central limit theorem for the sum of vector-valued functions of independent variables”, Theory Probab. Appl., 26:4 (1982), 773–786
R. Michel, “Necessary and sufficient conditions on rates of convergence in the multidimensional central limit theorem”, Manuscripta Math, 28:4 (1979), 361
V. I. Rotar', “Non-classical estimates of the convergence rate in the multidimensional central limit theorem. II”, Theory Probab. Appl., 23:1 (1978), 50–62
V. I. Rotar', “Nonclassical estimates of the rate of convergence in the multidimensional central limit theorem. I”, Theory Probab. Appl., 22:4 (1978), 755–772
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