摘要
设{εt;t∈Z+}是一严平稳零均值的LPQD随机变量序列,并且0<Eε12<∞,σ2=Eε12+2sum from j=2 to ∞ (Eε1εj),0<σ2<∞,{aj;j∈N}是一实数序列,满足sum from j=0 to ∞ |aj|<∞.定义线性过程Xt=sum from j=0 to ∞ (ajεt-j),t≥1,并令Sn=sum from t=1 to n Xt,Mn=max|Sk|,k≤n n≥1.利用弱收敛定理和矩不等式,对一般的拟权函数和边界函数,证明了{Mn}和{Sn}的精确渐近性.
Let｜εt;t∈Z^＋｜be a strictly stationary sequence of LPQD random variables with mean zeros, let0〈Eε^21〈∞,and σ^2=Eε^21＋2 ^∞∑j=2 Eε1εj,with0〈σ^2〈∞,{aj;j∈N}is a sequence of real numbers satisfying^∞∑j=0｜aj｜〈∞ Define a linear processX1=^∞∑j=0 ajεt-j,t≥1,and let Sn=^n∑t=1Xt,Mn=maxk≤n,n≥1.In this article, by means of the weak convergence theorems and moment inequalities, the precise asymptotics of { Mn } and { Sn } is proved for more general weighted functions and boundary functions.
出处
《吉林大学学报（理学版）》
CAS
CSCD
北大核心
2009年第2期251-256,共6页
Journal of Jilin University:Science Edition
基金
国家自然科学基金(批准号:10571073)
关键词
线性过程
LPQD列
精确渐近性
部分和
linear processes
LPQD sequences
precise asymptotics
partial sum
