关于遍历测度乘积的遍历性

本文利用拟特征标序列收敛的零一律与遍历测度的关系,讨论了遍历测度乘积的遍历性．     

拓扑遍历映射

本文研究紧致度量空间上拓扑遍历自映射的性质、判定及与混沌的关系．     

遍历定理的应用--一类极限的求法

作为遍历理论的应用,讨论一类极限的求法.     

拓扑遍历与拓扑双重遍历

令X为紧致度量空间,f:X→X为连续映射,U,V为X的任意非空开集,若{n>0|fn(U)∩V≠ )为正上密度集,则称f拓扑遍历.f拓扑双重遍历意味着f×f拓扑遍历.本文在[2]的基础上进一步讨论拓扑遍历与拓扑双重遍历映射的性质.     

半环上集函数的可列可加性

本文讨论半环上有限可加测度的可列可加性,得到一上连续有限可加测度成为可列可加的充要条件.此外还给出了[1]中一个基本结果的反例.     

迭代函数系统的遍历性质—Elton定理的改进

本文改进Elton定理的结论,得到迭代函数系统的几个新的遍历定理。     

无穷迭代函数系统的遍历定理

度量空间的压缩映射的一个集合称为一个迭代函数系统．凝聚迭代函数系统可以被看成无穷迭代函数系统．研究了紧度量空间上的无穷迭代函数系统．利用Banach极限的特性和均匀压缩性,证明了紧度量空间上无穷迭代函数系统的随机迭代算法满足遍历性．于是,凝聚迭代函数系统的随机迭代算法也满足遍历性．     

IFS中一个经典遍历性质的一些推广

该文针对概率迭代函数系统(IFS),给出一些遍历性质,这些结果推广了Elton[2]的结果,一个结果在某种意义上与Fustenberg[4]和Assani [1]关于弱混合系统中的结果类似.     

齐次马氏链强弱遍历等价关系的一种证明

主要给出齐次马氏链强遍历和弱遍历等价关系的一个直接证明.     

Ergodic properties of triangle partitions

We study the ergodic properties of a map called the Triangle Sequence. We prove that the algorithm is weakly convergent almost surely, and ergodic. As far as we know, it is the first example of a 2-dimensional algorithm where a surprising diophantine phenomenon happens: there are sequences of nested cells whose intersection is a segment, although no vertex is fixed. Examples of n-dimensional algorithms presenting this behavior were known for n ≥ 3.      

An Ergodic Decomposition Defined by Transition Probabilities

Our main goal in this paper is to prove that any transition probability P on a locally compact separable metric space (X,d) defines a Kryloff-Bogoliouboff-Beboutoff-Yosida (KBBY) ergodic decomposition of the state space (X,d). Our results extend and strengthen the results of Chap. 5 of Hernández-Lerma and Lasserre (Markov Chains and Invariant Probabilities, [2003]) and extend our KBBY-decomposition for Markov-Feller operators that we have obtained in Chap. 2 of our monograph (Zaharopol in Invariant Probabilities of Markov-Feller Operators and Their Supports, [2005]). In order to deal with the decomposition that we present in this paper, we had to overcome the fact that the Lasota-Yorke lemma (Theorem 1.2.4 in our book (op. cit.)) and two results of Lasota and Myjak (Proposition 1.1.7 and Corollary 1.1.8 of our work (op. cit.)) are no longer true in general in the non-Feller case. In the paper, we also obtain a “formula” for the supports of elementary measures of a fairly general type. The result is new even for Markov-Feller operators. We conclude the paper with an outline of the KBBY decomposition for a fairly large class of transition functions. The results for transition functions and transition probabilities seem to us surprisingly similar. However, as expected, the arguments needed to prove the results for transition functions are significantly more involved and are not presented here. We plan to discuss the KBBY decomposition for transition functions with full details in a small monograph that we are currently trying to write. I am indebted to Sean Meyn for a discussion that we had in November 2004, which helped me to significantly improve the exposition in this paper, and to two anonymous referees for useful recommendations.     

Ergodic theorems for random clusters

We prove pointwise ergodic theorems for a class of random measures which occurs in Laplacian growth models, most notably in the anisotropic Hastings–Levitov random cluster models. The proofs are based on the theory of quasi-orthogonal functions and uniform Wiener–Wintner theorems.     

A Conditional CLT which Fails for Ergodic Components

We show that the conditional central limit theorem can take place for a stationary process defined on a nonergodic dynamical system while this last does not satisfy the central limit theorem for any ergodic component. There exists an ergodic Markov chain such that the conditional central limit theorem is satisfied for an invariant measure but fails to hold for almost all starting points.      

广义算子半群的遍历及概率逼近定理

首先给出了广义算子半群的Abel-遍历和Cesaro-遍历的定义,对两种遍历的性质进行了刻画,研究了两种遍历的等价条件.其次,利用Pettis积分、算子值数学期望及广义连续修正模等工具给出广义算子半群的概率逼近表达式.     

Banach空间中非Lipschitzian交换非线性拓扑半群的遍历理论

本文在满足opial条件或存在Frechet可微范数的一致凸Banach空间中,给出了非Lipschitzian交换拓扑半群的遍历收敛定理及弱收敛定理.     

Ergodic Theorems and Ergodic Decomposition for Markov Chains

This paper considers Markov chains on a locally compact separable metricspace, which have an invariant probability measure but with no otherassumption on the transition kernel. Within this context, the limit providedby several ergodic theorems is explicitly identified in terms of the limitof the expected occupation measures. We also extend Yosidasergodic decomposition for Feller-like kernels to arbitrarykernels, and present ergodic results for empirical occupation measures, aswell as for additive-noise systems.     

超扩散过程的遍历定理

考虑初始测度为Ｌｅｂｅｓｇｕｅ测度μ 的一致椭圆超扩散过程，其分枝特征为ψ（狓，狕）＝犫（狓）狕＋γ（狓）狕２．该文研究这类超过程的占位时过程的极限性质．对系数犫（狓）及γ（狓）做必要的限制，得到了占位时过程在空间维数犱≤２的遍历定理，我们的结果是［６］的补充．     

Weighted and Ergodic Theorems for Series of Differences of Convolutions

We extend some results of C. Demeter about the boundedness of series of difference of convolutions to the setting of one-sided A _p weights. We need to use a different approach. To be precise, we prove that the kernel of the associated operator satisfies a generalized Hörmander condition. The weighted inequalities allow us to transfer the result to the ergodic case, when the operator is induced by a mean bounded, invertible, positive groups.