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


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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T1 - Precise asymptotics in the law of the logarithm for random fields in Hilbert space
A1 - FU Ke-ang
A1 - ZHANG Li-xin
J0 - Journal of Zhejiang University Science A
VL - 8
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SP - 651
EP - 659
%@ 1673-565X
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2007.A0651

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


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