On Kersting's proof of the central limit theorem

By an adaptation of a method originally invented by G. Kersting [1] for the calculation of the limiting distribution of Markovian processes the central limit theorem (CLT) is proven. Only the case of equal variances is considered.     

An elementary proof of the local central limit theorem

We give an elementary proof of the local central limit theorem for independent, non-identically distributed, integer valued and vector valued random variables.Support by a NSF Grant.Supported by an NSERC Grant     

极限的一个定理及其应用(英文)

给出了一个极限定理,能较好地解决一类特殊“和式”的极限问题.同时,利用对数函数的性质,又能够用来解决一些“积式”的极限.     

一维紧邻时间随机环境下可逗留随机游动的有关性质

给出了可数状态空间中时间随机环境下可逗留随机游动的一个统一模型,对于一维紧邻时间随机环境下的随机游动,在一定的条件下,讨论它的极限性质和中心极限定理,该结论类似于空间随机环境下的随机游动的有关结论.     

Asymptotic behavior of a tagged particle in simple exclusion processes

We review in this article central limit theorems for a tagged particle in the simple exclusion process. In the first two sections we present a general method to prove central limit theorems for additive functional of Markov processes. These results are then applied to the case of a tagged particle in the exclusion process. Related questions, such as smoothness of the diffusion coefficient and finite dimensional approximations, are considered in the last section.     

Almost sure central limit theorems for random fields

A general almost sure limit theorem is presented for random fields. It is applied to obtain almost sure versions of some (functional) central limit theorems. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multidimensional local central limit theorem of some non-uniformly hyperbolic systems

We consider Young＇s nonuniformly hyperbolic system （X, T, u） where u is the SRB measure corresponding to the system （X, T）, and show that if the components of a Holder observable f ： X → R^d are cohomologously independent, then f satisfies the multidimensional central limit theorem. Moreover if f is aperiodic, then f satisfies the local multidimensional central limit theorem.     

Central limit theorem and almost sure central limit theorem for the product of some partial sums

In this paper, we give the central limit theorem and almost sure central limit theorem for products of some partial sums of independent identically distributed random variables.     

任意随机组列的强极限定理

本文研究了任意随机组列的极限性质.利用构造鞅的方法得到了任意随机组列的强极限定理,所得结果摊广了任意随机适应序列和树上非齐次马氏链的强极限定理.     

马尔可夫骨架过程的极限分布

本文运用基本更新定理和Smith关键更新定理等理论和方法,对马尔可夫骨架过程的极限分布进行深入研究,得到主要结果如下:去掉了原有结果中要求的绝对连续的条件,给出了马尔可夫骨架过程极限分布存在的充分条件;得到了马尔可夫骨架过程极限分布的具体公式,并证明了该极限分布为概率分布.