设{Xn,n≥1}为独立同分布的正平方可积随机变量序列,其共同分布为连续的中尾分布.对于固定的常数a>0,令Sn=∑ from i=1 to n Xi,Mn=max(1≤i≤n)Xi,Sn(a)=∑ from i=1 to n XiI{Mn-a<Xi≤Mn},截断和Tn(a)=Sn-Sn(a).利用弱收敛定...设{Xn,n≥1}为独立同分布的正平方可积随机变量序列,其共同分布为连续的中尾分布.对于固定的常数a>0,令Sn=∑ from i=1 to n Xi,Mn=max(1≤i≤n)Xi,Sn(a)=∑ from i=1 to n XiI{Mn-a<Xi≤Mn},截断和Tn(a)=Sn-Sn(a).利用弱收敛定理和连续映射定理证明了截断和乘积的不变原理.展开更多
Let {X, X_; ∈N^d} be a field of i.i.d, random variables indexed by d-tuples of positive integers and taking values in a Banach space B and let X_^((r))=X_(m) if ‖X_‖ is the r-th maximum of {‖X_‖; ≤. Let S_=∑(≤...Let {X, X_; ∈N^d} be a field of i.i.d, random variables indexed by d-tuples of positive integers and taking values in a Banach space B and let X_^((r))=X_(m) if ‖X_‖ is the r-th maximum of {‖X_‖; ≤. Let S_=∑(≤)X_ and ^((r))S_=S_-(X_^((1))+…+X_^((r)). We approximate the trimmed sums ^((r))_n, by a Brownian sheet and obtain sufficient and necessary conditions for ^((r))S_ to satisfy the compact and functional laws of the iterated logarithm. These results improve the previous works by Morrow (1981), Li and Wu (1989) and Ledoux and Talagrand (1990).展开更多
Let {X_n, n≥1} be a sequence of iidrvs with a common df F and for every n, let X_(n,1)≤…≤X_(n,n) denote the order statistics of X_1,…, X_n. Consider the sums S_n~* =sum from k=k_n+1 to l_n(X_n,k), n≥1, where k_n...Let {X_n, n≥1} be a sequence of iidrvs with a common df F and for every n, let X_(n,1)≤…≤X_(n,n) denote the order statistics of X_1,…, X_n. Consider the sums S_n~* =sum from k=k_n+1 to l_n(X_n,k), n≥1, where k_n and l_n satisfy k_n/(n+1)→a and l_n/(n+1)→b for some 0<a<b<1.This paper gives necessary and sufficient conditions for (S_n~*- (n+1) M(k_n/(n+1), l_n/(n+1))/(n+1)^(1/2)to converge weakly to a df G, whereM(s, t) = integral from n=s to t(F^-(w)dw) forr 0<s<t<1;F^-(t) = inf{x:F(x)≥t}.展开更多
对一列独立同分布平方可积的随机变量序列{X_n,n≥1},当随机变量的分布具有中尾分布时,讨论了其截断和T_n(a)的随机乘积的渐近正态性质,其中T_n(a)=S_n-S_n(a),n= 1,2,…,S_n(a)=sum from j=1 to n X_jI{M_n-a<X_j≤M_n},a为某一大...对一列独立同分布平方可积的随机变量序列{X_n,n≥1},当随机变量的分布具有中尾分布时,讨论了其截断和T_n(a)的随机乘积的渐近正态性质,其中T_n(a)=S_n-S_n(a),n= 1,2,…,S_n(a)=sum from j=1 to n X_jI{M_n-a<X_j≤M_n},a为某一大于零的常数,M_n={X_k}.展开更多
设{X_n,n≥1}为i.i.d.r.v.S.,|X_n^(1)|≥|X_n^(2)|≥…≥|X_n^(n)|为{X_i,i≤n}的次序统计量,g为(0,+∞)上正Borel可测函数。我们讨论了截断和^(r)S_n=sum from i=r+t to nX_n^(i)与次序统计量X_n^(r)的比的分布收敛,令(r)T_n=[^(r)S_n...设{X_n,n≥1}为i.i.d.r.v.S.,|X_n^(1)|≥|X_n^(2)|≥…≥|X_n^(n)|为{X_i,i≤n}的次序统计量,g为(0,+∞)上正Borel可测函数。我们讨论了截断和^(r)S_n=sum from i=r+t to nX_n^(i)与次序统计量X_n^(r)的比的分布收敛,令(r)T_n=[^(r)S_n-(n-r)EX_1I{E|X_1|<+∞}]/g(|X_n(r)|),对正的常数列b_n,n≥1,我们得到了对所有的r≥1,^(r)T_n/(?)依分布收敛的充要条件。展开更多
设{X,X_n;n≥1}是一独立同分布的随机变量序列.如果|X_m|是新序列{|X_k|;k≤n}中的第r大元素,则令X_n^((r)=X_m.同时记部分和与修整和分别为S_n=sum from k=1 to n X_k和^((r))S_n=S_n-(X_n^((1))+…+X_n^((r))).该文在EX^2可能是无穷...设{X,X_n;n≥1}是一独立同分布的随机变量序列.如果|X_m|是新序列{|X_k|;k≤n}中的第r大元素,则令X_n^((r)=X_m.同时记部分和与修整和分别为S_n=sum from k=1 to n X_k和^((r))S_n=S_n-(X_n^((1))+…+X_n^((r))).该文在EX^2可能是无穷的条件下,得到了修整和^((r))S_n的广义强逼近定理.作为应用,建立了关于修整和以及修整和乘积的广义泛函重对数律.展开更多
We obtain an ahnost sure central limit theorem(ASCLT)for heavily trimmed sums.We also prove a function-typed ASCLT under the same conditions that assure measurable functions to satisfy the ASCLT for the partial sums o...We obtain an ahnost sure central limit theorem(ASCLT)for heavily trimmed sums.We also prove a function-typed ASCLT under the same conditions that assure measurable functions to satisfy the ASCLT for the partial sums of i.i.d,random variables with EX_1=0,EX_1~2=1.展开更多
Let{X n}be a sequence of random variables and X n1X n2…X nn their order statistics.In this paper a central limit theorem and a strong law of large numbers for randomly trimmed sums T n=βn i=αn+1 X ni are establishe...Let{X n}be a sequence of random variables and X n1X n2…X nn their order statistics.In this paper a central limit theorem and a strong law of large numbers for randomly trimmed sums T n=βn i=αn+1 X ni are established in the case thatαn andβn are positive integer-valued random variables such thatαn/n andβn/n converge to random variablesαandβrespectively with 0α<β1 in certain sense,and{X n}is aφ-mixing sequence.展开更多
where α_n and β_n are integers with 0≤α_n【β_n≤n. For an i.i.d, sequence {X_n}, many authors studied the asymptotic behavior of the trimmed sums T_n. In this note, we try extending the research extent in two dir...where α_n and β_n are integers with 0≤α_n【β_n≤n. For an i.i.d, sequence {X_n}, many authors studied the asymptotic behavior of the trimmed sums T_n. In this note, we try extending the research extent in two directions. First, we assume that {X_n} is φ-mixing.Moreover, α_n and β_n may be positive integer-valued random variables satisfying the convergence of the trimming fractions α_n/n and β_n/n to random variables α and β respectively with 0≤α【β≤1 in some sense. It seems to have not been studied for these two cases. A central limit theorem for this kind of randomly trimmed sum is established. Moreover we also show a strong law of large numbers.展开更多
文摘设{Xn,n≥1}为独立同分布的正平方可积随机变量序列,其共同分布为连续的中尾分布.对于固定的常数a>0,令Sn=∑ from i=1 to n Xi,Mn=max(1≤i≤n)Xi,Sn(a)=∑ from i=1 to n XiI{Mn-a<Xi≤Mn},截断和Tn(a)=Sn-Sn(a).利用弱收敛定理和连续映射定理证明了截断和乘积的不变原理.
基金Supported by National Natural Science Foundation of China (No. 10071072)
文摘Let {X, X_; ∈N^d} be a field of i.i.d, random variables indexed by d-tuples of positive integers and taking values in a Banach space B and let X_^((r))=X_(m) if ‖X_‖ is the r-th maximum of {‖X_‖; ≤. Let S_=∑(≤)X_ and ^((r))S_=S_-(X_^((1))+…+X_^((r)). We approximate the trimmed sums ^((r))_n, by a Brownian sheet and obtain sufficient and necessary conditions for ^((r))S_ to satisfy the compact and functional laws of the iterated logarithm. These results improve the previous works by Morrow (1981), Li and Wu (1989) and Ledoux and Talagrand (1990).
文摘Let {X_n, n≥1} be a sequence of iidrvs with a common df F and for every n, let X_(n,1)≤…≤X_(n,n) denote the order statistics of X_1,…, X_n. Consider the sums S_n~* =sum from k=k_n+1 to l_n(X_n,k), n≥1, where k_n and l_n satisfy k_n/(n+1)→a and l_n/(n+1)→b for some 0<a<b<1.This paper gives necessary and sufficient conditions for (S_n~*- (n+1) M(k_n/(n+1), l_n/(n+1))/(n+1)^(1/2)to converge weakly to a df G, whereM(s, t) = integral from n=s to t(F^-(w)dw) forr 0<s<t<1;F^-(t) = inf{x:F(x)≥t}.
文摘对一列独立同分布平方可积的随机变量序列{X_n,n≥1},当随机变量的分布具有中尾分布时,讨论了其截断和T_n(a)的随机乘积的渐近正态性质,其中T_n(a)=S_n-S_n(a),n= 1,2,…,S_n(a)=sum from j=1 to n X_jI{M_n-a<X_j≤M_n},a为某一大于零的常数,M_n={X_k}.
文摘设{X_n,n≥1}为i.i.d.r.v.S.,|X_n^(1)|≥|X_n^(2)|≥…≥|X_n^(n)|为{X_i,i≤n}的次序统计量,g为(0,+∞)上正Borel可测函数。我们讨论了截断和^(r)S_n=sum from i=r+t to nX_n^(i)与次序统计量X_n^(r)的比的分布收敛,令(r)T_n=[^(r)S_n-(n-r)EX_1I{E|X_1|<+∞}]/g(|X_n(r)|),对正的常数列b_n,n≥1,我们得到了对所有的r≥1,^(r)T_n/(?)依分布收敛的充要条件。
文摘设{X,X_n;n≥1}是一独立同分布的随机变量序列.如果|X_m|是新序列{|X_k|;k≤n}中的第r大元素,则令X_n^((r)=X_m.同时记部分和与修整和分别为S_n=sum from k=1 to n X_k和^((r))S_n=S_n-(X_n^((1))+…+X_n^((r))).该文在EX^2可能是无穷的条件下,得到了修整和^((r))S_n的广义强逼近定理.作为应用,建立了关于修整和以及修整和乘积的广义泛函重对数律.
基金Supported by the National Natural Science Foundation of China(No.10071003)Beijing Municipal Education Commission(KM200310028107)
文摘We obtain an ahnost sure central limit theorem(ASCLT)for heavily trimmed sums.We also prove a function-typed ASCLT under the same conditions that assure measurable functions to satisfy the ASCLT for the partial sums of i.i.d,random variables with EX_1=0,EX_1~2=1.
文摘Let{X n}be a sequence of random variables and X n1X n2…X nn their order statistics.In this paper a central limit theorem and a strong law of large numbers for randomly trimmed sums T n=βn i=αn+1 X ni are established in the case thatαn andβn are positive integer-valued random variables such thatαn/n andβn/n converge to random variablesαandβrespectively with 0α<β1 in certain sense,and{X n}is aφ-mixing sequence.
基金Project supported by the National Natural Science Foundation of Chinathe Natural Science Foundation of Zhejiang Province.
文摘where α_n and β_n are integers with 0≤α_n【β_n≤n. For an i.i.d, sequence {X_n}, many authors studied the asymptotic behavior of the trimmed sums T_n. In this note, we try extending the research extent in two directions. First, we assume that {X_n} is φ-mixing.Moreover, α_n and β_n may be positive integer-valued random variables satisfying the convergence of the trimming fractions α_n/n and β_n/n to random variables α and β respectively with 0≤α【β≤1 in some sense. It seems to have not been studied for these two cases. A central limit theorem for this kind of randomly trimmed sum is established. Moreover we also show a strong law of large numbers.
