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

作　　者：FU Ke-ang ZHANG Li-xin 

机构地区：[1]Department of Mathematics, Zhejiang University, Hangzhou 310027, China

出　　处：《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》2007年第4期651-659,共9页浙江大学学报（英文版）A辑（应用物理与工程）

基　　金：Project (No. 10471126) supported by the National Natural Science Foundation of China

摘　　要：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 =∑K≤nXK,K,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↓ 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 Spataru, 2003）.Consider the positive d-dimensional lattice d+ (d≥2) with partial ordering ≤, let {XK; K ∈ d+} be i.i.d. random vari- ables taking values in a real separable Hilbert space (H, ||·||) with mean zero and covariance operator ∑, and set partial sums SN =∑K≤NXK, K , N ∈ 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).

关 键 词：The law of the logarithm Random field Hilbert space. Tail probabilitv. Truncation method 

分 类 号：O211.4[理学—概率论与数理统计]