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Strong Law of Large Numbers for Array of Rowwise AANA Random Variables 被引量:1
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作者 CHEN Zhi-yong LIU Ting-ting WANG Xue-jun LI Xiao-qin 《Chinese Quarterly Journal of Mathematics》 CSCD 2014年第4期475-485,共11页
In this article, the strong laws of large numbers for array of rowwise asymptotically almost negatively associated(AANA) random variables are studied. Some sufficient conditions for strong laws of large numbers for ar... In this article, the strong laws of large numbers for array of rowwise asymptotically almost negatively associated(AANA) random variables are studied. Some sufficient conditions for strong laws of large numbers for array of rowwise AANA random variables are presented without assumption of identical distribution. Our results extend the corresponding ones for independent random variables to case of AANA random variables. 展开更多
关键词 AANA random variables array of rowwise AANA random variables strong law of large numbers
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Strong Law of Large Numbers for a 2-Dimensional Array of Pairwise Negatively Dependent Random Variables
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作者 Karn Surakamhaeng Nattakarn Chaidee Kritsana Neammanee 《Open Journal of Statistics》 2013年第1期42-46,共5页
In this paper, we obtain the strong law of large numbers for a 2-dimensional array of pairwise negatively dependent random variables which are not required to be identically distributed. We found the sufficient condit... In this paper, we obtain the strong law of large numbers for a 2-dimensional array of pairwise negatively dependent random variables which are not required to be identically distributed. We found the sufficient conditions of strong law of large numbers for the difference of random variables which independent and identically distributed conditions are regarded. In this study, we consider the limit as which is stronger than the limit as m× n→?∞ when m, n →?∞?are natural numbers. 展开更多
关键词 STRONG law of Large NUMBERS Negatively Dependent 2-Dimensional array of random variables
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PRECISE ASYMPTOTICS IN SELF-NORMALIZED SUMS OF ITERATED LOGARITHM FOR MULTIDIMENSIONALLY INDEXED RANDOM VARIABLES 被引量:3
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作者 Jiang Chaowei Yang Xiaorong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2007年第1期87-94,共8页
In the case of Z+^d(d ≥ 2)-the positive d-dimensional lattice points with partial ordering ≤, {Xk,k∈ Z+^d} i.i.d, random variables with mean 0, Sn =∑k≤nXk and Vn^2 = ∑j≤nXj^2, the precise asymptotics for ∑... In the case of Z+^d(d ≥ 2)-the positive d-dimensional lattice points with partial ordering ≤, {Xk,k∈ Z+^d} i.i.d, random variables with mean 0, Sn =∑k≤nXk and Vn^2 = ∑j≤nXj^2, the precise asymptotics for ∑n1/|n|(log|n|dP(|Sn/Vn|≥ε√log log|n|) and ∑n(logn|)b/|n|(log|n|)^d-1P(|Sn/Vn|≥ε√log n),as ε↓0,is established. 展开更多
关键词 multidimensionally indexed random variable precise asymptotics self-normalized sum Davislaw of large numbers law of iterated logarithm.
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ON THE ONE-SIDED LOGARITHMIC LAW FOR ARRAYS
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作者 QI Yongcheng(Department of Probability and Statistics, Peking University, Beijing 100871, China) 《Systems Science and Mathematical Sciences》 SCIE EI CSCD 1999年第2期123-132,共10页
This paper studies the one-sided logarithmic law for arrays of independent random variables and derives the necessary and sufficient condition for it in the case where the random variables are lid.
关键词 logarithmic law array of random variables.
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PRECISE RATE IN THE LAW OF ITERATED LOGARITHM FOR ρ-MIXING SEQUENCE 被引量:8
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作者 Huang Wei Zhang Lixin Jiang YeDept.of Math.,Zhejiang Univ.,Hangzhou 310028,China. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2003年第4期482-488,共7页
Let {X,X n;n≥1} be a strictly stationary sequence of ρ-mixing random variables with mean zero and finite variance. Set S n=n k=1X k,M n=max k≤n|S k|,n≥1. Suppose lim n→∞ES2 n/n=∶σ2>0 and ∞... Let {X,X n;n≥1} be a strictly stationary sequence of ρ-mixing random variables with mean zero and finite variance. Set S n=n k=1X k,M n=max k≤n|S k|,n≥1. Suppose lim n→∞ES2 n/n=∶σ2>0 and ∞n=1ρ 2/d(2n)<∞, where d=2,if -1<b<0 and d>2(b+1),if b≥0. It is proved that,for any b>-1, limε0ε 2(b+1)∞n=1(loglogn)bnlognP{M n≥εσ2nloglogn}= 2(b+1)πГ(b+3/2)∞k=0(-1)k(2k+1) 2b+2,where Г(·) is a Gamma function. 展开更多
关键词 mixing random variable law of iterated logarithm tail probabilities
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Some Limit Theorems for Weighted Sums of Random Variable Fields 被引量:2
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作者 GAN Shixin CHEN Pingyan 《Wuhan University Journal of Natural Sciences》 CAS 2006年第2期323-327,共5页
Let{Xn^-,n^-∈N^d}be a field of Banach space valued random variables, 0 〈r〈p≤2 and{an^-,k^-, (n^-,k^-) ∈ N^d × N^d ,k^-≤n^-} a triangular array of real numhers, where N^d is the d-dimensional lattice (d... Let{Xn^-,n^-∈N^d}be a field of Banach space valued random variables, 0 〈r〈p≤2 and{an^-,k^-, (n^-,k^-) ∈ N^d × N^d ,k^-≤n^-} a triangular array of real numhers, where N^d is the d-dimensional lattice (d≥1 ). Under the minimal condition that {||Xn^-|| r,n^- ∈N^d} is {|an^-,k^-|^r,(n^-,k^-)} ∈ N^d ×N^d,k^-≤n^-}-uniformly integrable, we show that ∑(k^-≤n^-)an^-,k^-,Xk^-^(L^r(or a,s,)→0 as |n^-|→∞ In the above, if 0〈r〈1, the random variables are not needed to be independent. If 1≤r〈p≤2, and Banach space valued random variables are independent with mean zero we assume the Banaeh space is of type p. If 1≤r≤p≤2 and Banach space valued random variables are not independent we assume the Banach space is p-smoothable. 展开更多
关键词 Banaeh space of type p multidimensional index strong law of large numbers L" convergence weightedsums of random variable fields martingale difference array
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Precise Rates in the Law of Iterated Logarithm for the Moment of I.I.D. Random Variables 被引量:11
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作者 Ye JIANG Li Xin ZHANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2006年第3期781-792,共12页
Let{X,Xn;n≥1} be a sequence of i,i.d, random variables, E X = 0, E X^2 = σ^2 〈 ∞.Set Sn=X1+X2+…+Xn,Mn=max k≤n│Sk│,n≥1.Let an=O(1/loglogn).In this paper,we prove that,for b〉-1,lim ε→0 →^2(b+1)∑n=1... Let{X,Xn;n≥1} be a sequence of i,i.d, random variables, E X = 0, E X^2 = σ^2 〈 ∞.Set Sn=X1+X2+…+Xn,Mn=max k≤n│Sk│,n≥1.Let an=O(1/loglogn).In this paper,we prove that,for b〉-1,lim ε→0 →^2(b+1)∑n=1^∞ (loglogn)^b/nlogn n^1/2 E{Mn-σ(ε+an)√2nloglogn}+σ2^-b/(b+1)(2b+3)E│N│^2b+3∑k=0^∞ (-1)k/(2k+1)^2b+3 holds if and only if EX=0 and EX^2=σ^2〈∞. 展开更多
关键词 the law of iterated logarithm strong approximation truncation method i.i.d random variables
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Laws of the Iterated Logarithm for-mixing Random Variables with Normal Distribution 被引量:1
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作者 Qun-ying WU 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2016年第2期385-394,共10页
Consider a ρ-mixing sequence of identically distributed random variables with the underlying dis- tribution in the domain of attraction of the normal distribution. This paper proves that law of the iterated logarithm... Consider a ρ-mixing sequence of identically distributed random variables with the underlying dis- tribution in the domain of attraction of the normal distribution. This paper proves that law of the iterated logarithm holds for ρ-mixing sequences of random variables. Our results generalize and improve Theorems 1.2-1.3 of Qi and Cheng (1996) from the i.i.d, case to ρ-mixing sequences. 展开更多
关键词 ρ-mixing sequence of random variables law of the iterated logarithm domain of attraction
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Limiting Behavior of Weighted Sums of NOD Random Variables 被引量:3
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作者 De Hua QIU Ping Yan CHEN 《Journal of Mathematical Research and Exposition》 CSCD 2011年第6期1081-1091,共11页
The strong laws of large numbers and laws of the single logarithm for weighted sums of NOD random variables are established.The results presented generalize the corresponding results of Chen and Gan [5] in independent... The strong laws of large numbers and laws of the single logarithm for weighted sums of NOD random variables are established.The results presented generalize the corresponding results of Chen and Gan [5] in independent sequence case. 展开更多
关键词 NOD random variables strong laws of large numbers laws of single logarithm weighted sums.
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NA随机变量对数律的收敛速度
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作者 邱德华 赵倩君 《应用概率统计》 CSCD 北大核心 2023年第5期659-666,共8页
设{X,X_(n),n>1}是同分布的NA随机变量序列,h(·)>0是定义在(0,∞)上的不减函数且满足∫_(1)^(∞)[th(t)^(-1)dt=∞.令ψ(t)=∫_(1)^(t)[sh(s)]^(-1)ds,t≥1,S_(n)=Σ_(i=1)^(n)X_(i),n≥1,Lt=ln max{e,t}.本文证明了Σ_(n)^(... 设{X,X_(n),n>1}是同分布的NA随机变量序列,h(·)>0是定义在(0,∞)上的不减函数且满足∫_(1)^(∞)[th(t)^(-1)dt=∞.令ψ(t)=∫_(1)^(t)[sh(s)]^(-1)ds,t≥1,S_(n)=Σ_(i=1)^(n)X_(i),n≥1,Lt=ln max{e,t}.本文证明了Σ_(n)^(∞)=1[nh(n)]^(-1)P(max_(1)≤j≤n|S_(j)|≥(1+ε)σ√2nLψ(n))<∞,∀ε>0成立的充要条件是E(X)=0和E(X^(2))=σ^(2)∈(0,∞).这一结果部分地推广了文献[7]的结论. 展开更多
关键词 NA随机变量 对数律 收敛速度
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不同分布WOD随机变量序列的重对数律 被引量:5
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作者 蔡光辉 潘雪艳 《高校应用数学学报(A辑)》 CSCD 北大核心 2015年第4期425-431,共7页
在一个独立随机变量序列的重对数律的基础上,获得了一个不同分布WOD随机变量序列的重对数定理,定理的证明基于一个Kolmogorov型指数不等式.
关键词 不同分布 WOD随机变量序列 重对数律
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阵列滑动和的强收敛性 被引量:3
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作者 陈平炎 管总平 《数学物理学报(A辑)》 CSCD 北大核心 2010年第6期1394-1401,共8页
该文获得了独立同分布随机变量阵列滑动平均和的对数律成立的充分必要条件,推广了已有的结果.
关键词 对数律 滑动平均和 独立同分布随机变量阵列
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在最少条件下的对数律精确渐近性(英文) 被引量:2
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作者 张立新 林正炎 《应用概率统计》 CSCD 北大核心 2006年第3期311-320,共10页
设X_1,X_2,…为独立同分布随机变量,记S_n=X_1+…+X_n,M_n=(?)|S_k|,n(?)1.本文在充分必要条件下给出了M_n和S_n的对数律之精确渐近性.
关键词 独立随机变量和的尾概率 对数律 强逼近
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NA随机变量序列加权和的Chover型重对数律 被引量:1
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作者 邱德华 陈平炎 《数学物理学报(A辑)》 CSCD 北大核心 2014年第3期674-683,共10页
利用NA随机变量的指数不等式,对于具有重尾分布的同分布的NA随机变量序列,得到了用积分检验来刻划其加权部分和的极限定理,作为推论还得到了Chover型重对数律.把这些结果应用到经典的可和方式,获得了相应的结果.这些结果推广了已知的一... 利用NA随机变量的指数不等式,对于具有重尾分布的同分布的NA随机变量序列,得到了用积分检验来刻划其加权部分和的极限定理,作为推论还得到了Chover型重对数律.把这些结果应用到经典的可和方式,获得了相应的结果.这些结果推广了已知的一些结论. 展开更多
关键词 NA随机变量 重尾分布 重对数律 积分检验 加权部分和
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关于NA随机变量极限定理的注记
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作者 刘立新 梅长林 《数学进展》 CSCD 北大核心 2006年第4期441-448,共8页
NA随机变量是一包含独立随机变量在内的有广泛应用的随机变量类,本文在一些更弱的条件下,建立了具有不同分布NA随机变量列的强大数律和有界重对数律,进而推广了已有的关于NA随机变量的结果。
关键词 NA随机变量 强大数律 有界重对数律
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ANA随机变量序列重对数矩收敛的精确渐近性
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作者 谭希丽 郭爽 《北华大学学报(自然科学版)》 CAS 2019年第5期594-599,共6页
设{X n,n≥1}为一列严平稳的ANA随机变量序列,利用ANA随机变量序列的中心极限定理和矩不等式,在适当的条件下给出了ANA随机变量序列重对数矩收敛的精确渐近性.
关键词 ANA随机变量序列 重对数律 矩收敛 精确渐近性
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Fuk-Nagaev型不等式的推广及应用
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作者 杨长森 蹇明 《应用数学》 CSCD 2000年第1期122-128,共7页
本文首先对具有 p( 1 <p≤ 2 )阶矩的独立 B值随机变量列 {Xn}研究了 Fuk-Nagaev型不等式 。
关键词 Fuk-Nagaev型 不等式 B值随机元 重对数律
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关于可交换随机变量序列的重对数律
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作者 赵月旭 《应用数学》 CSCD 北大核心 2002年第3期116-119,共4页
本文讨论了可交换随机变量序列 {Xn:n≥ 1 }的重对数律 .
关键词 可交换随机变量序列 重对数律
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离散随机变量序列的强偏差定理
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作者 王学武 《纯粹数学与应用数学》 CSCD 2009年第1期195-202,共8页
利用分析方法建立了用不等式表示的用对数似然比刻划的任意相依离散随机变量序列的强偏差定理,作为推论得到了更一般的离散随机变量序列加权和的强大数定律.
关键词 对数似然比 离散随机变量 强偏差定理 强大数定律
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A LIL for independent non-identically distributed random variables in Banach space and its applications 被引量:2
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作者 LIU WeiDong FU KeAng ZHANG LiXin 《Science China Mathematics》 SCIE 2008年第2期219-232,共14页
In this paper,we prove a general law of the iterated logarithm (LIL) for independent non-identically distributed B-valued random variables.As an interesting application,we obtain the law of the iterated logarithm for ... In this paper,we prove a general law of the iterated logarithm (LIL) for independent non-identically distributed B-valued random variables.As an interesting application,we obtain the law of the iterated logarithm for the empirical covariance of Hilbertian autoregressive processes. 展开更多
关键词 law of the iterated logarithm independent random variable autoregressive Hilbertian processes covariance operator 60F15
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