Almost sure central limit theory for products of sums of partial sums

Consider a sequence of i.i.d.positive random variables.An universal result in almost sure limit theorem for products of sums of partial sums is established.We will show that the almost sure limit theorem holds under a fairly general condition on the weight dk= k-1 exp（lnβk）,0≤β〈1.And in a sense,our results have reached the optimal form.

ON THE LIMITING BEHAVIOR OF THE MAXIMUM PARTIAL SUMS FOR ARRAYS OF ROWWISE NA RANDOM VARIABLES

Let {Xni, 1 ≤ n,i 〈 ∞} be an an array of rowwise NA random variables and {an, n ≥ 1} a sequence of constants with 0 〈 an ↑∞ . The limiting behavior of maximum partial sums 1/an max 1≤k≤n｜^k∑i=1 Xni｜ is investigated and some new results are obtained. The results extend and improve the corresponding theorems of rowwise independent random variable arrays by Hu and Taylor [1] and Hu and Chang [2].

Joint asymptotic distribution of exceedances point process and partial sum of stationary Gaussian sequence

Let {Xi}i=1^∞ be a standardized stationary Gaussian sequence with covariance function τ（n） =EX1Xn＋1, Sn =∑i=1^nXi,and X^-n=Sn/n.And let Nn be the point process formed by the exceedances of random level （x/√2 log n＋√2 log n-log（4π log n）/2√log n） √1-τ（n） ＋ X^-n by X1,X2,…, Xn. Under some mild conditions, Nn and Sn are asymptotically independent, and Nn converges weakly to a Poisson process on （0,1].

SELF-NORMALIZED CENTRAL LIMIT THEOREM AND ESTIMATION OF VARIANCE OF PARTIAL SUMS FOR NEGATIVE DEPENDENT RANDOM VARIABLES

Let ｛X n,n≥1｝ be a stationary LNQD or NA sequence satisfying EX 1=μ,EX 2 1<∞ and (Var S n)/n→σ 2 as n→∞.In this paper a class of self-normalized central limit theorems and estimators of Var S n are studied.The weak and strong consistency of the estimators of Var S n are presented.

On the Limiting Behavior of Weighted Partial Sums for B Valued Martingale Difference Sequences

Let {Xn, n≥1} be a martingale difference sequence and {a nk , 1?k?n,n?1} an array of constant real numbers. The limiting behavior of weighted partial sums ∑ k=1 n a nk X k is investigated and some new results are obtained.

Complete Convergence for Partial Sums of the Squares of ARCH Sequence

In this paper,we discuss the suffcient condition for complete convergence of partial sums of squares of the ARCH sequence,at the same time a moment inequality of maximum partial sums for squares of the ARCH sequence is proved.

Moments of the maximum of normed partial sums of ρ^--mixing random variables

Let {Xn,n ≥ 1} be a sequence of identically distributed ρ^--mixing random variables and set Sn =∑i^n=1 Xi,n ≥ 1,the suffcient and necessary conditions for the existence of moments of supn≥1 ｜Sn/n^1/r｜^p（0 〈 r 〈 2,p 〉 0） are given,which are the same as that in the independent case.

ON UNIFORM APPROXIMATION BY PARTIAL SUMS OF JACOBI SERIES ON ELLIPTIC REGION

In this paper, we discuss the relation between the partial sums of Jacobi serier on an elliptic region and the corresponding partial sums of Fourier series. From this we derive a precise approximation formula by the partial sums of Jacobi series on an elliptic region.

A Note on the Almost Sure Central Limit Theorem for Partial Sums of ρ^(−)-Mixing Sequences

Let be a strictly stationary sequence of ρ?-mixing random variables. We proved the almost sure central limit theorem, containing the general weight sequences, for the partial sums , where , . The result generalizes and improves the previous results.

Joint Limit Distributions of Exceedances Point Processes and Partial Sums of Gaussian Vector Sequence

In this paper, we study the joint limit distributions of point processes of exceedances and partial sums of multivariate Gaussian sequences and show that the point processes and partial sums are asymptotically independent under some mild conditions. As a result, for a sequence of standardized stationary Gaussian vectors, we obtain that the point process of exceedances formed by the sequence （centered at the sample mean） converges in distribution to a Poisson process and it is asymptotically independent of the partial sums. The asymptotic joint limit distributions of order statistics and partial sums are also investigated under different conditions.

Studentized Increments of Partial Sums

Using suitable self-normalization for partial sums of i.i.d.random variables,Griffin and Kuelbs established the law of the iterated logarithm for all distributions in the domain of attraction of a normal law.We obtain the corresponding results for Studentized increments of partial sums under thesame condition.

Moment inequalities for the partial sums of random variables

This paper discusses the conditions under which Rosenthal type inequality is obtained from M-Z-B type inequality. And M-Z-B type inequality is proved for a wide class of random variables. Hence Rosenthal type inequalities for some classes of random variables are obtained.

Almost Sure Central Limit Theorem for Partial Sums of Markov Chain

The authors prove an almost sure central limit theorem for partial sums based on an irreducible and positive recurrent Markov chain using logarithmic means,which realizes the extension of the almost sure central limit theorem for partial sums from an i.i.d.sequence of random variables to a Markov chain.

An Improved Result in Almost Sure Central Limit Theory for Products of Partial Sums with Stable Distribution

Consider a sequence of i.i.d.positive random variables with the underlying distribution in the domain of attraction of a stable distribution with an exponent in (1,2].A universal result in the almost sure limit theorem for products of partial sums is established. Our results significantly generalize and improve those on the almost sure central limit theory previously obtained by Gonchigdanzan and Rempale and by Gonchigdanzan.In a sense,our results reach the optimal form.

HOW SMALL ARE THE INCREMENTS OF PARTIAL SUMS OF NON-IID RANDOM VARIABLES

Csorgo and Revesz (1981) obtained an elegant result on how ismall the increments ofpartial sums of IID random variables are. But their proof seems some wrong. In this paperwe have not only corrected their proof, but also established the corresponding result forindependent, not necessarily identically distributed random variables under more generaland weaker assumptions.

Binary digit representation of moments for maximum partial sums of random variables and applications

Binary digit representation of partial sums for random variables has been investigated, and a good upper bound of moments of maximum partial sums for random variables has been reduced by using this representation. As an applications, stability and strong law of large numbers have been discussed. Many known classical results have been refined.

一个新的涉及一个多重可变上限函数和一个部分和的半离散Hilbert型不等式

应用权函数的方法,Euler-Maclaurin求和公式,Abel部分求和公式及实分析技巧,求出了一个新的涉及一个多重可变上限函数和一个部分和的半离散Hilbert型不等式.作为应用,考虑了特殊参数下不等式中最佳常数因子联系多参数的等价条件及一些特殊不等式.

基于背景间运算的部分已知概念构造

概念是利用形式概念分析进行知识获取的基础。在不完备形式背景中,为了表达“一定具有”以及“可能具有”的关系,概念的外延或内涵通常以区间集的形式表达,称这样的概念为部分已知概念。由部分已知概念的定义可知,其本质与不完备背景的最小和最大完备化有关,因而考虑对最小和最大完备化背景进行运算来寻找部分已知概念。通过将不完备形式背景的最小完备化与最大完备化分别进行并置和叠置构造两个新背景,其概念格分别同构于SE-ISI概念格和ISE-SI概念格,从而提出了构建SE-ISI概念格和ISE-SI概念格的新方法。对于ISE-ISI概念,使用不完备形式背景的最小与最大完备化的直和运算构造了新的形式背景,基于此背景提出了寻找ISE-ISI概念的方法。

POSITIVITY AND BOUNDEDNESS OF TRIGONOMETRIC SUMS

We give a systematic account of results which assure positivity and boundedness of partial sums of cosine or sine series. New proofs of recent results are sketched.

对于调和级数sum from n=1 to ∞(1/n)的分析

调和级数 ∑∞n =11n 是一种比较简单的发散级数 ,有关它发散性的证明 。