Let {Xn,n ≥ 1} be a strictly stationary LNQD （LPQD） sequence of positive random variables with EX1 = μ 〉 0, and VarX1 = σ^2 〈 ∞. Denote by Sn = ∑i=1^n Xi and γ = σ/μ the coefficients of variation. In this ...Let {Xn,n ≥ 1} be a strictly stationary LNQD （LPQD） sequence of positive random variables with EX1 = μ 〉 0, and VarX1 = σ^2 〈 ∞. Denote by Sn = ∑i=1^n Xi and γ = σ/μ the coefficients of variation. In this paper, under some suitable conditions, we show that a general law of precise asymptotics for products of sums holds. It can describe the relations among the boundary function, weighted function, convergence rate and limit value in the study of complete convergence.展开更多
设{εt;t∈Z+}是一严平稳零均值的LPQD随机变量序列,并且0<Eε12<∞,σ2=Eε12+2sum from j=2 to ∞ (Eε1εj),0<σ2<∞,{aj;j∈N}是一实数序列,满足sum from j=0 to ∞ |aj|<∞.定义线性过程Xt=sum from j=0 to ∞ (a...设{εt;t∈Z+}是一严平稳零均值的LPQD随机变量序列,并且0<Eε12<∞,σ2=Eε12+2sum from j=2 to ∞ (Eε1εj),0<σ2<∞,{aj;j∈N}是一实数序列,满足sum from j=0 to ∞ |aj|<∞.定义线性过程Xt=sum from j=0 to ∞ (ajεt-j),t≥1,并令Sn=sum from t=1 to n Xt,Mn=max|Sk|,k≤n n≥1.利用弱收敛定理和矩不等式,对一般的拟权函数和边界函数,证明了{Mn}和{Sn}的精确渐近性.展开更多
设{X_i,i≥1}是一严平稳零均值LPQD随机变量序列,0<EX_1~2<∞,σ~2=EX_1~2+sum from j=2 to ∞(E(X_1X_j)),并且0<σ~2<∞,令S_n=sum from i=1 to n(X_i),利用部分和S_n的弱收敛定理,证明了当ε→0时,sum from n≥1 to(n^(r...设{X_i,i≥1}是一严平稳零均值LPQD随机变量序列,0<EX_1~2<∞,σ~2=EX_1~2+sum from j=2 to ∞(E(X_1X_j)),并且0<σ~2<∞,令S_n=sum from i=1 to n(X_i),利用部分和S_n的弱收敛定理,证明了当ε→0时,sum from n≥1 to(n^(r/p-2))P〔│S_n│≥εn^(1/p)〕,sum from n≥1 to(1/n)P〔│S_n│≥εn^(1/p)〕,sum from n≥1 to((1n n)~δ/n)P〔│S_n│≥ε(n 1n n)～(1/2)〕的精确渐近性.展开更多
基金Supported by National Natural Science Foundation of China (Grant No. 10571073)
文摘Let {Xn,n ≥ 1} be a strictly stationary LNQD （LPQD） sequence of positive random variables with EX1 = μ 〉 0, and VarX1 = σ^2 〈 ∞. Denote by Sn = ∑i=1^n Xi and γ = σ/μ the coefficients of variation. In this paper, under some suitable conditions, we show that a general law of precise asymptotics for products of sums holds. It can describe the relations among the boundary function, weighted function, convergence rate and limit value in the study of complete convergence.
文摘设{εt;t∈Z+}是一严平稳零均值的LPQD随机变量序列,并且0<Eε12<∞,σ2=Eε12+2sum from j=2 to ∞ (Eε1εj),0<σ2<∞,{aj;j∈N}是一实数序列,满足sum from j=0 to ∞ |aj|<∞.定义线性过程Xt=sum from j=0 to ∞ (ajεt-j),t≥1,并令Sn=sum from t=1 to n Xt,Mn=max|Sk|,k≤n n≥1.利用弱收敛定理和矩不等式,对一般的拟权函数和边界函数,证明了{Mn}和{Sn}的精确渐近性.
文摘设{X_i,i≥1}是一严平稳零均值LPQD随机变量序列,0<EX_1~2<∞,σ~2=EX_1~2+sum from j=2 to ∞(E(X_1X_j)),并且0<σ~2<∞,令S_n=sum from i=1 to n(X_i),利用部分和S_n的弱收敛定理,证明了当ε→0时,sum from n≥1 to(n^(r/p-2))P〔│S_n│≥εn^(1/p)〕,sum from n≥1 to(1/n)P〔│S_n│≥εn^(1/p)〕,sum from n≥1 to((1n n)~δ/n)P〔│S_n│≥ε(n 1n n)～(1/2)〕的精确渐近性.
