Integro-local CLT for sums of independent nonlattice random vectors
Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 1, pp. 36-52 Cet article a éte moissonné depuis la source Math-Net.Ru

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A number of results are refined in the integro-local central limit theorem in the case of sums of independent nonlattice random vectors.
Keywords: central limit theorem, independent random vectors, volume of a Borel set, asymptotic expansions, integro-local theorems.
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L. V. Rozovskii. Integro-local CLT for sums of independent nonlattice random vectors. Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 1, pp. 36-52. http://geodesic.mathdoc.fr/item/TVP_2019_64_1_a2/

[1] C. Stone, “A local limit theorems for nonlattice multi-dimensional distribution functions”, Ann. Math. Statist., 36:2 (1965), 546–551 | DOI | MR | Zbl

[2] C. Stone, “On local and ratio limit theorems”, Proceedings of the 5th Berkeley symposium on mathematical statistics and probability (Berkeley, Calif., 1965/66), v. 2, Contributions to probability theory, Part 2, Univ. California Press, Berkeley, Calif., 1967, 217–224 | MR | Zbl

[3] A. A. Borovkov, A. A. Mogul'skii, “Integro-local theorems for sums of independent random vectors in the series scheme”, Math. Notes, 79:4 (2006), 468–482 | DOI | DOI | MR | Zbl

[4] A. A. Borovkov, “Integro-local and local theorems on normal and large deviations of sums of nonidentically distributed random variables in the triangular array scheme”, Theory Probab. Appl., 54:4 (2010), 571–587 | DOI | DOI | MR | Zbl

[5] A. A. Borovkov, “Generalization and refinement of the integro-local Stone theorem for sums of random vectors”, Theory Probab. Appl., 61:4 (2017), 590–612 | DOI | DOI | MR | Zbl

[6] A. A. Borovkov, K. A. Borovkov, “A refined version of the integro-local Stone theorem”, Statist. Probab. Lett., 123 (2017), 153–159 | DOI | MR | Zbl

[7] R. N. Bhattacharya, R. Ranga Rao, Normal approximation and asymptotic expansions, Wiley Ser. Probab. Math. Statist., John Wiley Sons, New York–London–Sydney, 1976, xiv+274 pp. | MR | MR | Zbl | Zbl

[8] V. V. Petrov, Sums of independent random variables, Ergeb. Math. Grenzgeb., 82, Springer-Verlag, New York–Heidelberg, 1975, x+346 pp. | DOI | MR | MR | Zbl | Zbl

[9] L. V. Rozovskii, “Otsenki skorosti skhodimosti v “intervalnoi” TsPT dlya summ nezavisimykh sluchainykh vektorov”, Vestn. SPbGU. Ser. 1. Matem. Mekh. Astron., 4(62):3 (2017), 466–476 | MR

[10] L. V. Rozovskii, “Ob asimptoticheskikh razlozheniyakh v “intervalnoi” TsPT dlya summ nezavisimykh sluchainykh vektorov”, Veroyatnost i statistika. 26, Zap. nauch. sem. POMI, 466, POMI, SPb., 2017, 273–288 | MR

[11] G. M. Fichtenholz, Differential- und Integralrechnung, v. III, Hochschulbücher für Math., 63, 12., ber. Aufl., Johann Ambrosius Barth Verlag GmbH, Leipzig, 1992, 564 pp. | MR | Zbl

[12] A. Bikyalis, “Asimptoticheskie razlozheniya dlya raspredelenii summ nezavisimykh nereshetchatykh sluchainykh vektorov”, Litovskii matem. sb., 10:4 (1970), 673–679 | MR | Zbl

[13] H. Cramer, Random variables and probability distributions, Cambridge Tracts in Math. and Math. Phys., 36, Cambridge Univ. Press, 1937, viii+121 pp. | MR | Zbl