摘要
设{εt,t∈Z}为定义在同一概率空间(Ω,F,P)上的严平稳随机变量序列,满足Eε0=0,E|ε_0|~p<∞,对某个p>2,且满足强混合条件.{a_j,j∈Z}为一实数序列,满足sum from -∞ to ∞(|a_j|)<∞,sum from -∞ to ∞(a_j)≠0.令X_t=sum from -∞ to ∞(a_jε_(t-j))(t≥1),S_n=sum from 1 to n(X_t)(n≥1).利用由强混合序列生成的线性过程的弱收敛定理及矩不等式讨论了在bn=O(1/loglogn)的条件下,当∈→0时,P{|S_n|≥(∈+b_n)τ(2nloglogn)^(1/2)}的一类加权级数的收敛性质.
Let {εt,t∈Z} be a strictly stationary sequence defined on a probability space （Ω,f,p） such that Eε0=0, and E｜ε0｜^p〈∞, for some p 〉 2. And the sequence {εt,t∈Z}, is assumed to mixing conditions {aj,j∈Z} is a sequence of real numbers with ^∞∑j=-∞ ｜aj｜〈∞,^∞∑j=-∞ a≠0. Xt=^∞∑ j=-∞ ajε（t-j）（t≥1）,Sn=^n∑t=1 Xt（n≥1）. Using the weak convergence theorem of the linear process generated by strong mixing sequences and the moment inequaliti asymptotics of strong mixing sequences, we studied the precise asymptoties of a kind of weighted infinite series of P {｜Sn｜≥（∈＋bb）τ√2nlog log n } as ∈→0 under the conditions of bn=0（1/log log n）.
出处
《吉林大学学报（理学版）》
CAS
CSCD
北大核心
2007年第3期325-330,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
强混合序列
线性过程
重对数律
精确渐近性质
strong mixing sequences
linear process
the law of the iterated logarithm
precise asymptotics
