Precise rates in the law of the logarithm in the Hilbert space |
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| Authors: | Wei Huang Lixin Zhang |
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| Institution: | a School of Mathematics and Statistics, Carleton University, Ottawa, ON K1S 5B6, Canada
b Department of Mathematics, Zhejiang University, Hangzhou 310028, PR China |
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| Abstract: | Let  be a sequence of i.i.d. random variables taking values in a real separable Hilbert space (H,‖⋅‖) with covariance operator Σ, and set Sn=X1+?+Xn, n?1. Let  . We prove that, for any 1<r<3/2 and a>−d/2, |
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| Keywords: | Complete convergence Tail probabilities of sums of i i d random variables The law of the logarithm Strong approximation |
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