## BOUNDS FOR THE RATE OF STRONG APPROXIMATION IN THE MULTIDIMENSIONAL INVARIANCE PRINCIPLE

Götze F, Zaitsev AY (2009)
THEORY OF PROBABILITY AND ITS APPLICATIONS 53(1): 59-80.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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Autor*in
Götze, FriedrichUniBi; Zaitsev, A. Yu
Einrichtung
Abstract / Bemerkung
The goal of this paper is to derive consequences of the result of Zaitsev [Theory Probab. Appl., 45 (2001), pp. 624-642; 46 (2002), pp. 490-514; 676-698]. We establish bounds for the rate of strong Gaussian approximation of sums of independent R-d-valued random vectors xi(j) having finite moments E parallel to xi(j)parallel to(gamma), gamma >= 2. A multidimensional version of the results of Sakhanenko [Trudy Inst. Mat., 5 (1985), pp. 27-44 (in Russian)] is obtained.
Stichworte
multidimensional invariance principle; sums of; strong approximation; independent random vectors
Erscheinungsjahr
2009
Zeitschriftentitel
THEORY OF PROBABILITY AND ITS APPLICATIONS
Band
53
Ausgabe
1
Seite(n)
59-80
ISSN
0040-585X
Page URI
https://pub.uni-bielefeld.de/record/1634382

## Zitieren

Götze F, Zaitsev AY. BOUNDS FOR THE RATE OF STRONG APPROXIMATION IN THE MULTIDIMENSIONAL INVARIANCE PRINCIPLE. THEORY OF PROBABILITY AND ITS APPLICATIONS. 2009;53(1):59-80.
Götze, F., & Zaitsev, A. Y. (2009). BOUNDS FOR THE RATE OF STRONG APPROXIMATION IN THE MULTIDIMENSIONAL INVARIANCE PRINCIPLE. THEORY OF PROBABILITY AND ITS APPLICATIONS, 53(1), 59-80. https://doi.org/10.1137/S0040585X9798350X
Götze, Friedrich, and Zaitsev, A. Yu. 2009. “BOUNDS FOR THE RATE OF STRONG APPROXIMATION IN THE MULTIDIMENSIONAL INVARIANCE PRINCIPLE”. THEORY OF PROBABILITY AND ITS APPLICATIONS 53 (1): 59-80.
Götze, F., and Zaitsev, A. Y. (2009). BOUNDS FOR THE RATE OF STRONG APPROXIMATION IN THE MULTIDIMENSIONAL INVARIANCE PRINCIPLE. THEORY OF PROBABILITY AND ITS APPLICATIONS 53, 59-80.
Götze, F., & Zaitsev, A.Y., 2009. BOUNDS FOR THE RATE OF STRONG APPROXIMATION IN THE MULTIDIMENSIONAL INVARIANCE PRINCIPLE. THEORY OF PROBABILITY AND ITS APPLICATIONS, 53(1), p 59-80.
F. Götze and A.Y. Zaitsev, “BOUNDS FOR THE RATE OF STRONG APPROXIMATION IN THE MULTIDIMENSIONAL INVARIANCE PRINCIPLE”, THEORY OF PROBABILITY AND ITS APPLICATIONS, vol. 53, 2009, pp. 59-80.
Götze, F., Zaitsev, A.Y.: BOUNDS FOR THE RATE OF STRONG APPROXIMATION IN THE MULTIDIMENSIONAL INVARIANCE PRINCIPLE. THEORY OF PROBABILITY AND ITS APPLICATIONS. 53, 59-80 (2009).
Götze, Friedrich, and Zaitsev, A. Yu. “BOUNDS FOR THE RATE OF STRONG APPROXIMATION IN THE MULTIDIMENSIONAL INVARIANCE PRINCIPLE”. THEORY OF PROBABILITY AND ITS APPLICATIONS 53.1 (2009): 59-80.
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