| 鞅差序列生成的线性过程的精确渐近性 |
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| 引用本文： | 曾艳,王文胜.鞅差序列生成的线性过程的精确渐近性[J].高师理科学刊,2010,30(4):1-4. |
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| 作者姓名： | 曾艳 王文胜 |
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| 作者单位： | 杭州师范大学,理学院,浙江,杭州,310036 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 讨论了滑动平均过程∑+∞Xk=i=-∞aiξk-i,其中:{ξi,Fi;-∞i+∞}是均值为零的非平稳双侧无穷鞅差序列,{ai;-∞i+∞}为绝对可和的实数序列.记∑==nkSnXk1,E(ξi2Fi-1)=σ2∞,a.s.,∑+∞=-∞=iaai.证明了对每一i≥1,当B∈Fi,并且P(B)0时,在适当的矩条件下,对相当广泛的实值函数-(x)及正实数v,有()νννεlim0ε1/∑n1-′(nPSnεaσn-(n)B=EN1/∞→=),其中:N是服从标准正态分布的随机变量.
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| 关 键 词： | 非平稳鞅差序列 强大数定律 线性过程 精确渐近性 |
Precise asymptotics for linear processes of martingale difference sequences |
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| ZENG Yan,WANG Wen-sheng.Precise asymptotics for linear processes of martingale difference sequences[J].Journal of Science of Teachers＇College and University,2010,30(4):1-4. |
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| Authors: | ZENG Yan WANG Wen-sheng |
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| Institution: | ZENG Yan,WANG Wen-sheng(School of Science,Hangzhou Normal University,Hangzhou 310016,China) |
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| Abstract: | Discussed moving-linear process ∑ nonstationary martingale difference with mean zeros,{ a i ;-∞i＋∞} is an absolutely summable sequence of real numbers.Set ∑ = = n k Sn Xk 1,E（ξ i 2 Fi-1） =σ2∞,a.s.,∑ ＋∞ =-∞ = i a ai.Proved that,for every i ≥1,when B ∈ Fi,P（B）0,at the condition of appropriate moment,for quite a wide ranges of real-valued function-（x）and real numbersν,then（） ννν εl im0 ε 1/∑n1-＇（n PSn εaσn-（n）B=EN1/∞ → =）,where N is a random variable of the standard normal distribution. |
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| Keywords: | nonstationary martingale difference sequence law of large number moving-linear process precise asymptotics |
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