线性过程关于大数律的精确渐近性  

Precise Asymptotics in the Law of Large Numbers of Moving-average Processes

作　　者：李云霞[1] 

机构地区：[1]浙江财经学院,杭州310018

出　　处：《数学物理学报（A辑）》2006年第5期675-687,共13页Acta Mathematica Scientia

基　　金：浙江省教育厅2006年度科研基金(20060122)资助

摘　　要：该文主要讨论的是滑线性过程X_k=sum from i=-∞to∞a_(i+k)ε_i,其中{ε_i；-∞＜i＜∞}是均值为零,方差有限的双测无穷同分布■-混合或负相伴随机变量序列,{a_i；～∞＜i＜∞}为绝对可和的实数序列．令S_n=sum from k=1 to n X_k,n≥1,作者证明了,对于1≤p＜2以及r＞p,若E|ε_1|~r＜∞■ε^(2(r-p)/(2-p))sum from n=1 to∞n^(r/p-2)P{|S_n|≥εn^(1/p)}=p/(r-p)E|Z|^(2(r-p)/(2-p)),其中Z是服从均值为零,方差为τ~2=σ~2·(sum from i=-∞to∞．a_i)~2的正态分布．In this paper, the author discusses moving-average process Xk=^∞∑i=-∞ai＋kεi, where {εi;-∞〉i〈∞} is a doubly infinite sequence of identically distributed φ-mixing or negatively associated random variables with mean zeros and finite variances, {ai;-∞〉i〈∞} is an absolutely summable sequence of real numbers. Set Sn=^n∑k=1Xk,n≥1, the author proves that, if E｜ε1｜^r〈∞, then, for 1 ≤ p 〈 2 and τ 〉 p limε↓0 ε^2（τ-p）/（2-p）^∞∑n=1 n^τ/-2P{｜Sn｜}≥εn^1/p}=p/r-pE｜Z｜^）（τ-p）/（2-p）.where Z has a normal distribution with mean 0 and variance τ^2=σ^2,（^∞∑i=-∞,ai）^2.

关 键 词：线性过程 Φ-混合 负相伴 Baum-Katz律 完全收敛性 

分 类 号：O211[理学—概率论与数理统计]