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

摘要

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.