Multidimensional version of a result of Sakhanenko in the invariance principle for vectors with finite exponential moments. I. (English) Zbl 0994.60029

Zaitsev, A. Yu.

Theory Probab. Appl. 45, No. 4, 624-641 (2000) and Teor. Veroyatn. Primen. 45, No. 4, 718-738 (2000).

Sakhanenko (1984) generalized and improved the KMT results on the approximation of sums of i.i.d. random variables by sums of Gaussian random variables to the case of nonidentically distributed random variables. Otherwise, Einmahl (1989) extended the KMT result to the multidimensional case. In an earlier paper the author studied the multidimensional case for nonidentically distributed vectors. As he assumed identical covariance matrices an adequate generalization of the Sakhanenko result was still open. This generalization is now given in the present paper.

Reviewer: Fritz Liese (Rostock)

MSC:

60F15	Strong limit theorems
60F17	Functional limit theorems; invariance principles

Keywords:

multidimensional invariance principle; strong approximation