ρ-混合序列移动平均过程的完全矩收敛

本文利用ρ-混合序列移动平均过程的依分布收敛,以及ρ-混合序列的矩不等式,研究了ρ-混合序列移动平均过程的完全矩收敛,这些结果推广和改进了已知文献中相应的结论.     

随机环境中生灭过程首击间隔随机序列的性质

本文研究了随机环境中生灭过程首击间隔随机序列的性质，假设环境独立同分布，证明了{τn}n=1^∞是ψ-混合随机序列，但不是平稳序列，并求得期望E(τn)及其极限，这对于研究有关极限性质有关键作用．     

ρ~--混合序列部分和随机乘积的渐近分布

ρ~--混合序列是各种相依类型中较弱的一种,研究其极限性质具有一般意义.利用ρ~--混合序列部分和乘积的渐近分布及部分和最大值的矩不等式,得出了ρ~--混合序列部分和随机乘积的渐近分布.     

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.     

弱相依随机序列的若干新结果(英文)

设{Xn,n≥1}为-混合序列. 利用随机变量的截尾方法和-混合序列的三级数定理,讨论了-混合序列的收敛性质,并且得到了-混合序列的一类强极限定理,这些结果推广了独立序列的相应结果.最后研究了-混合序列加权和的强稳定性.     

SOME CONVERGENCE PROPERTIES FOR THE PARTIAL SUMS OF (ρ～) MIXING SEQUENCES

本文研究了(ρ～)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(ρ～)混合序列部分和的收敛性,并进一步得到了(ρ～)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.     

不同分布ρ混合序列乘积和的强收敛性

研究了ρ混合序列的收敛性质,利用得到的结果和ρ混合序列的矩不等式讨论了ρ混合序列乘积和的强收敛性质.     

混合随机变量序列加权和的矩完全收敛性

该文研究了混合随机变量序列加权和的矩完全收敛性.利用混合随机变量的Rosenthal型最大值不等式,得到了混合随机变量序列加权和的矩完全收敛性定理,这些结果推广和改进了已知的一些文献中相应结论.     

不同分布(p)混合序列的完全收敛性

讨论了一类比较广泛的相依随机变量序列(p)混合序列的收敛性质,推广了吴群英等人关于(p)混合序列的完全收敛性的研究,获得了不同分布p混合序列的完全收敛性的结果.     

■混合随机变量序列加权和的矩完全收敛性

本文研究了■混合随机变量序列加权和的矩完全收敛性,利用φ混合随机变量序列的Rosenthal型不等式,得到了■混合随机变量序列加权和的矩完全收敛性定理,这些结果推广和改进了已有的结果.     

On the asymptotic normality of sequences of weak dependent random variables

The aim of this paper is to investigate the asymptotic normality for strong mixing sequences of random variables in the absense of stationarity or strong mixing rates. An additional condition is imposed to the coefficients of interlaced mixing. The results are applied to linear processes of strongly mixing sequences. The class of applications include filters of certain Gaussian sequences.Supported in part by an NSF grant, cost-sharing from the University of Cincinnati, and a Taft research grant.     

Maximal Inequalities and an Invariance Principle for a Class of Weakly Dependent Random Variables

The aim of this paper is to investigate the properties of the maximum of partial sums for a class of weakly dependent random variables which includes the instantaneous filters of a Gaussian sequence having a positive continuous spectral density. The results are used to obtain an invariance principle for strongly mixing sequences of random variables in the absence of stationarity or strong mixing rates. An additional condition is imposed to the coefficients of interlaced mixing. The results are applied to linear processes of strongly mixing sequences.     

非平稳φ-混合序列强律收敛速度的进一步探讨

本文研究非平稳φ 混合序列的强大数律：无需混合速度限制，给出了完全收敛成立的充要条件；在弱混合速度条件下，讨论了Ｍａｒｃｉｎｋｉｅｗｉｃｚ Ｚｙｇｍｕｎｄ强律成立的必要条件，进而得出混合情形的Ｍａｒｃｉｎｋｉｅｗｉｃｚ Ｚｙｇｍｕｎｄ强律，其结果与独立情形相一致．     

Countable Partially Exchangeable Mixtures

Partially exchangeable sequences representable as mixtures of Markov chains are completely specified by de Finetti’s mixing measure. The paper characterizes, in terms of a subclass of hidden Markov models, the partially exchangeable sequences with mixing measure concentrated on a countable set, for sequences of random variables both on a discrete space and on a Polish space.     

■混合阵列行加权和最大值的若干收敛性质

讨论了■混合阵列行加权和最大值的弱收敛性、L_p收敛性和完全收敛性定理,将独立阵列的相关极限定理推广到了■混合随机阵列情形.     

Limit laws for the maximum and minimum of stationary sequences

Summary The class of non-degenerate joint limiting distributions for the maximum and minimum of stationary mixing sequences is determined. These limit distributions are of the form, H(x, ) –H(x, –y), where H(x,y) is a bivariate extreme value distribution. Unlike the classical result for i.i.d. sequences, the maximum and minimum of stationary mixing sequences may be asymptotically dependent. We also give a sufficient condition for the asymptotic independence of the maximum and minimum. Finally, an example of a stationary sequence satisfying the mixing condition D in Leadbetter but which is not weakly mixing is constructed.This research was supported in part by the National Science Foundation grant MCS 80-05483     

Holderian Weak Invariance Principle for Stationary Mixing Sequences

We provide some sufficient mixing conditions on a strictly stationary sequence in order to guarantee the weak invariance principle in Hölder spaces. Strong mixing and \(\rho \)-mixing conditions are investigated as well as \(\tau \)-dependent sequences. The main tools are deviation inequalities for mixing sequences.     

Eventually independent sequences

The class of eventually independent sequences for a weakly mixing transformation is an isomorphism invariant that is useful for distinguishing zero entropy transformations. This invariant is used to distinguish certain weakly mixing transformations as well as certain partially mixing transformations. In memory of Shlomo Horowitz Research partially supported by National Science Foundation Grant MCS7606735A01.     

Gaussian fluctuations for random walks in random mixing environments

We consider a class of ballistic, multidimensional random walks in random environments where the environment satisfies appropriate mixing conditions. Continuing our previous work [2] for the law of large numbers, we prove here that the fluctuations are Gaussian when the environment is Gibbsian satisfying the “strong mixing condition” of Dobrushin and Shlosman and the mixing rate is large enough to balance moments of some random times depending on the path. Under appropriate assumptions the annealed Central Limit Theorem (CLT) applies in both nonnestling and nestling cases, and trivially in the case of finite-dependent environments with “strong enough bias”. Our proof makes use of the asymptotic regeneration scheme introduced in [2]. When the environment is only weakly mixing, we can only prove that if the fluctuations are diffusive then they are necessarily Gaussian. Partially supported by CNRS, UMR 7599 “Probabilités et Modèles aléatoires”. Partially supported by NSF grant number DMS-0302230.