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

A. Yu. Zaitsev

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 68 (2013) no. 4, pp. 721-761

Résumé

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.

Détail

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

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