Estimates for the rate of strong approximation in Hilbert space |
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Authors: | F Götze A Yu Zaitsev |
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Institution: | 1.Bielefeld University,Bielefeld,Germany;2.St. Petersburg Department of the Steklov Mathematical Institute,St. Petersburg,Russia |
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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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Keywords: | |
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