This article is cited in 15 papers

Bounds for the Rate of Strong Approximation in the Multidimensional Invariance Principle

F. Götze^a, A. Yu. Zaitsev<sup>b

a</sup> Bielefeld University, Department of Mathematics
^b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: 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 $\mathbf{R}^d$-valued random vectors $\xi_j$ having finite moments $\mathbf{E}\|\xi_j\|^\gamma$, $\gamma\ge 2$. A multidimensional version of the results of Sakhanenko [Trudy Inst. Mat., 5 (1985), pp. 27–44 (in Russian)] is obtained.

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

Received: 31.07.2007

Language: English

DOI: 10.4213/tvp2484

 English version: Theory of Probability and its Applications, 2009, 53:1, 59–80

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