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.
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Original Russian Text Copyright © 2011 Götze F. and Zaitsev A. Yu.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 52, No. 4, pp. 796–808, July–August, 2011.
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Götze, F., Zaitsev, A.Y. Estimates for the rate of strong approximation in Hilbert space. Sib Math J 52, 628–638 (2011). https://doi.org/10.1134/S0037446611040070
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DOI: https://doi.org/10.1134/S0037446611040070