This article is cited in 4 papers

Estimates for the rate of strong approximation in Hilbert space

F. Götze^a, A. Yu. Zaitsev<sup>b

a</sup> Bielefeld University, Bielefeld, Germany
^b St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia

Abstract: We obtain infinite-dimensional corollaries of our recent results. We show that the finite-dimensional results imply meaningful estimates for the accuracy of strong Gaussian approximation of sums of independent identically distributed Hilbert space-valued random vectors with finite power moments. We establish that the accuracy of approximation depends substantially on the decay rate of the sequence of eigenvalues of the covariance operator of the summands.

Keywords: infinite-dimensional invariance principle, strong approximation, sums of independent random vectors, accuracy estimates for approximation.

UDC: 519.2

Received: 18.03.2011

 English version: Siberian Mathematical Journal, 2011, 52:4, 628–638

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