一类线性过程中的经验分布函数的收敛速度  

Rate of Convergence for the Empirical Distribution Function of a Broad Class of Linear Processes

作　　者：阮宏顺[1] 

机构地区：[1]江苏工业学院信息科学系,江苏常州213016

出　　处：《江苏工业学院学报》2005年第3期34-37,共4页Journal of Jiangsu Polytechnic University

摘　　要：涉及到一类平稳的线性过程中分布函数的一致收敛速度。考虑线性过程:X(n)=∞∑i=0δ(i)Z(n-i),在如下条件下:①Z(n)为i.i.d.r.v′s,且E|Z(n)|<+∞;②Z(n)的分布函数F具有有界密度;③参数δ(i)满足|δ(i)|<g(i),其中函数g满足∞∑i=1ig(i)<∞,给出了supx∈R|F(x)-^F(x)|→0的速度为N-12logNloglogN条件下,比文献[1]的速度N-21(logN)快。This paper deals with uniform rate of convergence for a broad class of stationary linear processes. In particular, the class is considered under the condition： ① a finite first absolute moment, ② the distribution function has bounded density, and ③ the parameters are bounded in absolute value by some function which satisfies. It is proved that the empirical distribution function converges to, uniformly in, at a rate which is faster than that of [1] under the same condition.

关 键 词：线性过程 分布函数 收敛速度 

分 类 号：O211[理学—概率论与数理统计]