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Journal of Zhejiang University SCIENCE A 2007 Vol.8 No.4 P.651~659

10.1631/jzus.2007.A0651


Precise asymptotics in the law of the logarithm for random fields in Hilbert space


Author(s):  FU Ke-ang, ZHANG Li-xin

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   fukeang@hotmail.com, stazlx@zju.edu.cn

Key Words:  The law of the logarithm, Random field, Hilbert space, Tail probability, Truncation method


FU Ke-ang, ZHANG Li-xin. Precise asymptotics in the law of the logarithm for random fields in Hilbert space[J]. Journal of Zhejiang University Science A, 2007, 8(4): 651~659.

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DOI - 10.1631/jzus.2007.A0651


Abstract: 
Consider the positive d-dimensional lattice Z+d (d≥2) with partial ordering ≤, let {XK; K∈Z+d be i.i.d. random variables taking values in a real separable hilbert space (H, ||∙||) with mean zero and covariance operator ∑, and set partial sums SN =∑KNXK, N∈Z+d. Under some moment conditions, we obtain the precise asymptotics of a kind of weighted infinite series for partial sums SN as ε↘0 by using the truncation and approximation methods. The results are related to the convergence rates of the law of the logarithm in hilbert space, and they also extend the results of (Gut and Spǎtaru, 2003).

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

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