On limit laws for sums of Pfeifer records

The problem of determining limiting distributions for sums of records has been studied by several authors who have considered a variety of assumptions sufficient to ensure that sums of records properly normalized will converge to a non-degenerate distribution. As a parallel to these endeavors, it is of interest to establish conditions under which the sum of Pfeifer records, properly normalized, converges. Pfeifer records are defined under the assumption that initial observations are i.i.d. with common survival function and following the (n−1)-th record value the observations are assumed to have survival function ,n=1,2,.... The study of the asymptotic behavior of sums of Pfeifer records constitutes a natural generalization of work on sums of classical records. The present paper introduces conditions under which the limit distribution of sums of Pfeifer records is non-degenerate.      

Asymptotic properties of near Pfeifer records

Asymptotic properties of the number of near records are known in the literature. We generalize these results to the Pfeifer model which has a wider application. In particular we establish convergence in probability, in the almost sure sense and in distribution for the number of near records under the Pfeifer model.     

Asymptotic Properties of Sums of Upper Records

Arnold and Villaseñor (1999) raised several questions for upper records, including characterizing all limit distributions of normalized partial sums of upper records. We provide some answers in the case when the distribution from which the samples are drawn is bounded above. When the distribution is not bounded above, we give sufficient conditions on the distribution for the properly normalized partial sums to converge to a standard normal distribution. We show that our conditions are general enough so that the examples provided by Arnold and Villaseñor (1999) are covered by our results.     

关于记录值序列部分和的渐近正态性

证明了 Burr分布和 Frechét分布的记录值序列的部分和是渐进对数正态的 ,从而解决了文[2 ]中的一个悬而未决的问题     

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.     

关于PA列部分和与乘积和的Marcinkiewicz型强大数律

Birkel(1989)d在方差存在的条件下，证明了不同分布PA列部分和的Kolmogorov型强大数律.本文取消了方差存在的限制，在合理的矩条件下证明了更一般的不同分布PA列部分和与乘积和的Marcinkiewicz型强大数律，从而能将独立列的相应结果作为自己的特况．     

关于不同分布两两NQD列的Jamison型加权乘积和的强稳定性

本文讨论了不同分布两两ＮＱＤ列的Ｊａｍｉｓｏｎ型加权乘积和的强稳定性及乘积和的Ｍａｒｃｉｎｋｉｅｗｉｃｚ型强大数律,推广并改进了Ｅｔｅｍａｄｉ［１］关于不同分布两两独立列部分和的工作及Ｍａｔｕｌａ［２］,王岳宝等［３］关于同分布两两ＮＱＤ列部分和的工作．     

α-混合序列部分和乘积精确渐近性的一般形式

利用前人获得的α-混合序列部分和乘积的渐近分布的结果,对一般的边界函数和拟权函数得到了α-混合序列部分和乘积的精确渐近性的一般形式.     

Weak convergence of partial sums of absolutely regular sequences

We show that weak convergence results for partial sums of absolutely regular sequences can easily be derived from the corresponding convergence results for independent triangular arrays. The link to be used is a simple lemma on the total variation norm.     

B值随机元和的完全收敛性

在B值随机元随机有界于一非负随机变量的情况下．讨论了B值独立随机元序列非随机足标和的完全收敛性，作为应用，得到了随机足标和完全收敛性的相应结果，将[5]中的一些结果推广到B值独立随机无情形，同时使[3]（d=1），[4]，[6]的相应结果成为特例．     

两类记录值之和的中心极限定理

该文给出了Ｌｏｇｉｓｔｉｃ分布纪录值序列部分和的中心极限定理；对于Ｐａｒｅｔｏ分布纪录值序列的部分和T_n，获得了ｌｎT_n的中心极限定理．这一工作不仅具有概率论的极限理论方面的研究价值，而且在金融、保险等领域也具有相当重要的应用前景．     

混合序列部分和的若干收敛性质

本文研究了混合序列部分和的若干收敛性质.利用Serfling不等式推广情形,证明了一类随机变量序列部分和的一个收敛性结果,获得了混合序列部分和的收敛性,并进一步得到了混合序列加权和的强收敛性和完全收敛性,推广并改进了文[2]中有关结果.     

两两NQD列加权和的安全收敛性

本文研究两两NQD系加权和的完全收敛性，证明了一般双下标加权系数的加权部分和的完全收敛性，改进了吴群英（2002）的结果。     

两两NQD列的Lp收敛性和完全收敛性

在较宽泛的条件下研究了不同分布两两NQD列加权和的收敛性质,利用矩不等式和截尾方法,获得了一般双下标加权系数的加权部分和的LP收敛性和完全收敛性定理,推广了前人的相应结果.     

A mixture-type limit theorem for nonlinear functions of Gaussian sequences

We show that, for a certain class of nonlinear functions of Gaussian sequences, the limiting distribution of normalized sums of the nonlinear function values of a sequence is the convolution of a Gaussian distribution with another non-Gaussian distribution.     

Record values in sequences of sample ranges

The classical representation of record values in sequences of independent random variables with the standard exponential distribution E(1) as sums of exponentially distributed random summands plays an important role in the mathematical theory of records. A generalization of this representation is proposed. A new similar result that makes it possible to express the record values of sample ranges as sums of independent exponentially distributed random variables is obtained.     

不同分布NA列乘积和的强收敛性

推广了Chow等人关于不同分布的r.v.列部分和强收敛的部分结果。得到了不同分布NA列乘积和强收敛的若干充分条件。     

正相协列乘积和的重对数律与强大数律

证明了强平稳正相协列乘积和的重对数律与不同分布正相协列乘积和的强大数律,指出了部分和服从强大数律但乘积和未必服从强大数律这一事实,并讨论了定理2中一个条件的必要性．     

Summation of multiple trigonometric series by generalized methods formulated using δ -like finite functions

We consider the generalized sums of multiple trigonometric series. We investigate the sufficient conditions of convergence of the series obtained by termwise differentiation of the series for Lebesgue integrable functions as well as the errors of approximation of functions by sequences of generalized partial sums of series.     

Convergence en loi et lois du logarithme itéré pour les vecteurs gaussiens

In this paper we prove a Strassen version of the law of the iterated logarithm for some sequences of weakly asymptotically independant Banach space valued gaussian random variables which converge in distribution, and we prove that the central limit theorem implies the functional form of the law of the iterated logarithm for the partial sums of certain Banach space valued gaussian sequences.Furthermore we give conditions for the convergence in distribution of sequences of gaussian random variables and gaussian stochastic processes, and these conditions permit us to prove that our results generalize in the gaussian case all similar results known to the authors at present.