线性过程关于大数律的精确渐近性

该文主要讨论的是滑线性过程 $X_k=sumlimits_{i=-infty}^infty a_{i+k}varepsilon_i$,其中 ${varepsilon_i; -infty$varphi$ -混合或负相伴随机变量序列,${a_i;-inftyp$, 若 $E|varepsilon_1|^r

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

In this paper, the author discusses moving-average process $X_k=sumlimits_{i=-infty}^infty a_{i+k}varepsilon_i$,where ${varepsilon_i; -infty $varphi$-mixing or negatively associated random variables with mean zeros and finite variances, ${a_i;-infty $S_n=sumlimits_{k=1}^nX_k, ngeq 1$, the author proves that, if $E|varepsilon_1|^rp$$$lim_{epsilonsearrow 0}epsilon^{2(r-p)/(2-p)}sumlimits_{n=1}^infty n^{r/p-2}P{|S_n|geq epsilonn^{1/p}}=frac{p}{r-p}E|Z|^{2(r-p)/(2-p)},$$ where $Z$ has a normal distribution with mean 0 and variance $tau^2=sigma^2cdot(sumlimits_{i=-infty}^infty a_i)^2.