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Integro-local CLT for sums of independent nonlattice random vectors. (English. Russian original) Zbl 1478.60091

Theory Probab. Appl. 64, No. 1, 27-40 (2019); translation from Teor. Veroyatn. Primen. 64, No. 1, 36-52 (2019).
Summary: A number of results are refined in the integro-local central limit theorem in the case of sums of independent nonlattice random vectors.

MSC:

60F05 Central limit and other weak theorems
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References:

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[10] L. V. Rozovsky, On asymptotic expansions in the “interval” CLT for sums of independent random vectors, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 466 (2017), Veroyatnost’ i Statistika. 26, pp. 273-288 (in Russian).
[11] G. M. Fichtenholz, Differential- und Integralrechnung. III, translated from the 1960 Russian original by L. Boll and K. Gröger, 12th ed., Hochschulbücher für Math. 63, Johann Ambrosius Barth Verlag GmbH, Leipzig, 1992.
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[13] H. Cramér, Random Variables and Probability Distributions, Cambridge Tracts in Math. Math. Phys. 36, Cambridge Univ. Press, Cambridge, 1937.
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