连续自映射及其扭扩半流的不变测度

本文研究了紧致度量空间上连续自映射及连续半流的不变测度,并且证明了如下结论:(1)在拓扑等价的无不动点的连续半流的不变测度之间以及在连续自映射及其扭扩半流的不变测度之间存在一一对应;(2)作为(1)的应用,给出如下结论(见[2,定理2.1]):“环面上无不动点的连续流是唯一遍历的当且仅当它至多有一条周期轨”一个易接受的证明.     

连续自映射及其扭扩半流的不变测度

本文研究了紧致度量空间上连续自映射及连续半流的不变测度,并且证明了如下结论(1)在拓扑等价的无不动点的连续半流的不变测度之间以及在连续自映射及其扭扩半流的不变测度之间存在一一对应;(2)作为(1)的应用,给出如下结论(见[2,定理2.1])"环面上无不动点的连续流是唯一遍历的当且仅当它至多有一条周期轨"一个易接受的证明.     

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.     

关于拉氏变换之微分性质的一点注记

反例说明拉氏变换的一条微分性质存在的错误,通过理论分析指出其问题所在,并给出改正。     

连续小波变换及小波框架算子的一些性质

以泛函分析的观点来考察连续小波变换及小波框架算子，得到了它们的一些性质，并给出了严格证明，弥补了有关献中的不足。     

UNIQUENESS, ERGODICITY AND UNIDIMENSIONALITY OF INVARIANT MEASURES UNDER A MARKOV OPERATOR

Let X be a compact metric space and C（X） be the space of all continuous functions on X. In this article, the authors consider the Markov operator T ： C（X）N C（X）N defined by
for any f = （f1,f2,… ,fN）, where （pij） is a N x N transition probability matrix and {wij } is an family of continuous transformations on X. The authors study the uniqueness, ergodicity and unidimensionality of T＊-invariant measures where T＊ is the adjoint operator of T.     

关于Misuirewing一个定理的注记

本文改进了Misuirewing的一个定理，并给出小熵猜测的一个新的证明。     

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。     

枢轴消去变换的若干性质

得到了与Gauss消去变换有着密切联系的枢轴消去变换的三个重要性质.     

Mixing Limit Theorems for Ergodic Transformations

We show that distributional and weak functional limit theorems for ergodic processes often hold for arbitrary absolutely continuous initial distributions. This principle is illustrated in the setup of ergodic sums, renewal-theoretic variables, and hitting times for ergodic measure preserving transformations.     

Ergodic Properties of Random Positive Semigroups

In this paper, we study the unique ergodicity of random positive semigroups and their asymptotic behavior as time tends to infinity.     

Certain Characterizations of Normal Distribution via Transformations

It is well known that i.i.d. (independent and identically distributed) normal random variables are transformed into i.i.d. normal random variables by any orthogonal transformation. Less well known are nonlinear transformations with the above-mentioned property. In this work we present nonlinear transformations preserving normality, which are more general than the existing ones in the literature.     

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．     

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.     

Matrix Transformations Between Some Vector-Valued Sequence Spaces

In this paper, we give necessary and sufficient conditions for infinite matrices mapping from the Nakano vector-valued sequence space (X, p) into any BK-space, and by using this result, we obtain the matrix characterizations from (X, p) into the sequence spaces (Y), c₀(Y, q), c(Y), _s(Y), E_r(Y), and F_r(Y), where p = (p_k) and q = (q_k) are bounded sequences of positive real numbers such that p_k 1 for all k N, r 0, and s 1.AMS Subject Classification (2000): 46A45     

Ergodic Behaviour of Nonconventional Ergodic Averages for Commuting Transformations

Based on T. Tao’s celebrated result on the norm convergence of multiple ergodic averages for commuting transformations, we find that there is a subsequence which converges almost everywhere. Meanwhile, we obtain the ergodic behaviour of diagonal measures, which indicates the time average equals the space average. According to the classification of transformations, we also give several different results. Additionally, on the torus Td with special rotation, we prove the pointwise convergence in Td, and get a result for ergodic behaviour.     

Ergodicity and strong limit results for two-time-scale functional stochastic differential equations

This article focuses on a class of two-time-scale functional stochastic differential equations, where the phase space of the segment processes is infinite-dimensional. The systems under consideration have a fast-varying component and a slowly varying one. First, the ergodicity of the fast-varying component is obtained. Then inspired by the Khasminskii’s approach, an averaging principle, in the sense of convergence in the pth moment uniformly in time within a finite time interval, is developed.     

The First-Order Nonholonomic Connections with the Galilean Groups of Local Transformations

In the canonical smooth fiber bundles : ^{n+1 n} endowed with the metric tensor fields of relevant structure, we consider natural representations of the Galilean groups and construct -invariant generalizations of differentiable connections. In both regular and special cases of the representations of the relevant groups , we found all the affine nonholonomic ₁-, ₂-, and _{1, 2}-connections of the first order (see [4]) possessing the local Lie groups of transformations and also described the respective -invariant planar connections.