A. Yu. Zaitsev, “The accuracy of strong Gaussian approximation for sums of independent random vectors”, Russian Math. Surveys, 68:4 (2013), 721

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Russian Mathematical Surveys, 2013, Volume 68, Issue 4, Pages 721–761
DOI: https://doi.org/10.1070/RM2013v068n04ABEH004851 (Mi rm9537)

This article is cited in 14 scientific papers (total in 14 papers)

The accuracy of strong Gaussian approximation for sums of independent random vectors

A. Yu. Zaitsev^ab

^a St. Petersburg State University
^b St. Petersburg Department of V. A. Steklov Institute of the Steklov Mathematical Institute, Russian Academy of Sciences

English version PDF (903 kB) Citations (14) Russian version article

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DOI: https://doi.org/10.1070/RM2013v068n04ABEH004851

Abstract: This paper is a survey of recent results on the accuracy of strong Gaussian approximation for sums of independent random vectors. They give multidimensional generalizations of one-dimensional results due to Komlós, Major, and Tusnády, as well as to Sakhanenko, and improve upon Einmahl's multidimensional results. Infinite-dimensional analogues of these results are also presented.
Bibliography: 102 titles.

Keywords: multidimensional invariance principle, strong approximation, sums of independent random vectors.

Funding agency	Grant number
Russian Foundation for Basic Research	13-01-00256
Ministry of Education and Science of the Russian Federation	НШ-1216.2012.01
Russian Academy of Sciences - Federal Agency for Scientific Organizations

Received: 09.04.2013

Bibliographic databases:

Document Type: Article

UDC: 519.2

MSC: 60F17

Language: English

Original paper language: Russian

Citation: A. Yu. Zaitsev, “The accuracy of strong Gaussian approximation for sums of independent random vectors”, Russian Math. Surveys, 68:4 (2013), 721–761

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/rm9537

https://doi.org/10.1070/RM2013v068n04ABEH004851

https://www.mathnet.ru/eng/rm/v68/i4/p129

This publication is cited in the following 14 articles:

Péter Bálint, Dalia Terhesiu, “Generalized law of the iterated logarithm for the Lorentz gas with infinite horizon”, Electron. J. Probab., 30:none (2025)
Matias D. Cattaneo, Michael Jansson, Xinwei Ma, “Local regression distribution estimators”, Journal of Econometrics, 240:2 (2024), 105074
C. Cuny, J. Dedecker, A. Korepanov, F. Merlevède, “Rates in Almost Sure Invariance Principle for Nonuniformly Hyperbolic Maps”, Commun. Math. Phys., 405:10 (2024)
Fabian Mies, Ansgar Steland, “Sequential Gaussian approximation for nonstationary time series in high dimensions”, Bernoulli, 29:4 (2023)
E. O. Lenena, “Accuracy of estimation of the vector of queue lengths for open Jackson networks”, Theory Probab. Appl., 67:4 (2022), 633–639
Elena Bashtova, Alexey Shashkin, “Strong Gaussian approximation for cumulative processes”, Stochastic Processes and their Applications, 150 (2022), 1
D. I. Blinova, M. A. Lifshits, “Energy of Taut Strings Accompanying a Wiener Process and Random Walk in a Band of Variable Width”, J Math Sci, 268:5 (2022), 573
Lifshits M.A., Siuniaev A.A., “Energy of Taut Strings Accompanying Random Walk”, Prob. Math. Stat.., 41:1 (2021), 9–23
Elena Bashtova, Elena Lenena, Springer Proceedings in Mathematics & Statistics, 371, Recent Developments in Stochastic Methods and Applications, 2021, 318
Cattaneo M.D., Farrell M.H., Feng Y., “Large Sample Properties of Partitioning-Based Series Estimators”, Ann. Stat., 48:3 (2020), 1718–1741
D. I. Blinova, M. A. Lifshits, “Energiya natyanutykh strun, soprovozhdayuschikh vinerovskii protsess i sluchainoe bluzhdanie v polose peremennoi shiriny”, Veroyatnost i statistika. 29, Zap. nauchn. sem. POMI, 495, POMI, SPb., 2020, 64–86
M. A. Lifshits, Ya. Yu. Nikitin, V. V. Petrov, A. Yu. Zaitsev, A. A. Zinger, “Toward the history of the Saint Petersburg school of probability and statistics. I. Limit theorems for sums of independent random variables”, Vestn. St Petersb. Univ. Math., 51:2 (2018), 144–163
A. Korepanov, “Rates in almost sure invariance principle for dynamical systems with some hyperbolicity”, Commun. Math. Phys., 363:1 (2018), 173–190
P. Kevei, D. M. Mason, “Couplings and strong approximations to time-dependent empirical processes based on i.i.d. fractional Brownian motions”, J. Theor. Probab., 30:3 (2017), 729–770

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	835
Russian version PDF:	434
English version PDF:	256
References:	62
First page:	14

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