一类线性过程中的分布函数的收敛速度  

Rate of Convergence for the 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》2003年第1期47-49,共3页Journal of Jiangsu Polytechnic University

基　　金：江苏省高校自然科学研究项目(02KJD110001);江苏工业学院科技基金资助

摘　　要：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)<∞,我们给出了supx∈R|F(x)-FVm(x)|→0的速度为(g(h(m)))1/2,在相同的条件下,比原速度(mg(h(m)))1/2快。This paper dealt with uniform rate of convergence for a broad class of stationary linear processes:X(n)=∑∞i=0δ(i)Z(n-i) was considered under the condition that ①Z(n)(n=1,2,…) is iidrv′s with a finite first absolute moment,②the distribution functionF of X(n) bounded density,and ③the parameters δ(i) were bounded in absolute value by some function g which satisfies ∑∞i=1ig(i)<∞.It was proved that the distribution function FVm(x) converged to F(x),uniformly in x,at a rate O((g(h(m)))1/2) as which was faster than that of [1] on the same condition.

关 键 词：线性过程 分布函数 收敛速度 一致收敛 

分 类 号：O173.1[理学—数学]