产出时间序列的遍历性

主要研究产出时间序列的遍历性质,得出了市场经济条件下产出时间序列是马氏过程的结论,并讨论了它的遍历态;证明了市场经济发展的周期状形态.     

周期离散动力系统的遍历定理

该文研究周期离散动力系统的遍历定理,把自治离散动力系统的遍历定理推广到周期系统,包括Hilbert空间上的平均遍历定理、von Neumann平均遍历定理和Birkhoff逐点遍历定理.     

马氏链集间转移的一类强大数定律

本文研究了马氏链从一个状态子集到另一个状态子集的转移概率的极限性质.利用Doob鞅收敛定理,获得了任意随机序列的强大数定律、马氏链泛函的强大数定律和强遍历定理.推广了马氏链传统转移概率的极限性质和强极限定理.     

基于离散观测下Cauchy-OU过程的最大似然估计

基于离散观测样本,本文研究Cauchy-OU过程的参数估计问题.在大多数情况下,离散时间的最大似然函数是不能直接计算出来的,因此采用傅里叶变换及Gaver-Stehfest算法,构造似然函数的一个显式逼近序列,且该序列收敛于真实(但未知)的似然函数.最后,采用最大似然估计法估计出未知参数.仿真实验表明,所得到的参数估计是比较准确且稳定的.     

离散时间Markov链的几何遍历速度

本文研究一般状态空间离散时间几何遍历Markov链的收敛速度.当状态空间中含有原子时,本文采用与可数状态空间类似的方法,即采用谱理论法研究几何遍历速度.对于不含原子的Markov链,先利用Nummelin分裂技术构造出含有原子的新Markov链,再建立新Markov链与原Markov链几何遍历速度的关系,最后由最小化条件和首次回返时的几何阶矩得到原Markov链几何遍历的收敛速度.进一步,本文将所得结果应用于研究Metropolis-Hastings算法.     

离散时间单死链的可加泛函北大核心CSCD

本文给出了离散单死链的可加泛函高阶矩的显式递推表达,并研究了离散单死链的多项式遍历和中心极限定理.     

离散指数分布序列的强偏差与强逼近

本文引入离散指数分布概念,建立了关于离散型指数分布序列的强偏差定理和强大数定律.同时,得到离散指数分布序列对连续指数分布序列的强逼近.     

混合体积、对数凹序列和B样条函数

本文主要通过样条函数方法研究与之相关的离散几何学和组合学问题.在离散几何学方面主要考虑超立方体切面(cube slicing)体积和混合体(mixed volume)的样条表示,利用B样条函数的几何解释,将超立方体切面问题转化为与之等价的样条函数问题,分别给出Laplace和P′olya关于超立方体切面定理的样条证明,将样条函数与混合体积联系起来,给出一类混合体积的样条解释.利用这种解释可以得到一类具有对数凹性质的组合序列,从而部分地回答了Schmidt和Simion所提出的关于混合体积的公开问题.在组合数学方面主要考虑多种组合多项式与样条函数的关联以及组合序列对数凹性质的样条方法研究.本文借助丰富的样条函数理论,不但验证了离散几何学和组合数学中很多现有的结果,而且得到了一系列离散数学对象的新性质,建立了离散数学问题与具有连续性特质的样条函数之间的内在联系.     

抽象空间中的 q-过程的遍历位势

<正> §1.引言Syski 在[1]中,对时齐的可数状态的遍历的马氏过程,在其二阶矩存在及其它条件下,证明了遍历位势核的存在性,并利用位势核的种种性质,改善了著名的 Riesz 分解定理.本文讨论的是时齐的一般状态的马氏过程,在强遍历的条件下,证明了遍历位势核的存在性,并得到了遍历位势核的一些性质.利用遍历位势核的存在性,改善了一般状态的马氏过程的 Riesz 分解定理.此外,还讨论了如何利用转移密度函数,寻找转移函数的遍历极限的问题.     

求解Oseen流的交替线松弛多重网格方法

利用Riemann解的通量差分分裂法——Godunov方法对Oseen流控制方程进行离散,得到了基于一阶上迎风格式的离散方程,并给出了使用多重网格方法求解该离散方程的V-循环算法和W-循环算法的收敛性分析.通过局部Fourier分析方法,对获得的离散方程的聚对称交替线GaussSeidel松弛的光滑性质进行了研究.结果表明:使用多重网格的两层网格及三层网格算法求解具有不同Reynolds数的Oseen流,即便是在高Reynolds数情况下,聚对称交替线Gauss-Seidel松弛具有很好的光滑性质,多重网格W-循环算法收敛性比V-循环算法好.     

Density-equicontinuity and Density-sensitivity

In this paper we introduce the notions of (Banach) density-equicontinuity and densitysensitivity. On the equicontinuity side, it is shown that a topological dynamical system is densityequicontinuous if and only if it is Banach density-equicontinuous. On the sensitivity side, we introduce the notion of density-sensitive tuple to characterize the multi-variant version of density-sensitivity. We further look into the relation of sequence entropy tuple and density-sensitive tuple both in measuretheoretical and topological setting, and it turns out that every sequence entropy tuple for some ergodic measure on an invertible dynamical system is density-sensitive for this measure; and every topological sequence entropy tuple in a dynamical system having an ergodic measure with full support is densitysensitive for this measure.     

Weak ergodicity and products of random matrices

A representation for a weakly ergodic sequence of (nonstochastic) matrices allows products of nonnegative matrices which eventually become strictly positive to be expressed via products of some associated stochastic matrices and ratios of values of a certain function. This formula used in a random setup leads to a representation for the logarithm of a random matrix product. If the sequence of random matrices is in addition stationary then automatically almost all sequences are weakly ergodic, and the representation is expressed in terms of an one-dimensional stationary process. This permits properties of products of random matrices to be deduced from the latter. Second moment assumptions guarantee that central limit theorems and laws of the iterated logarithm hold for the random matrix products if and only if they hold for the corresponding stationary process. Finally, a central limit theorem for some classes of weakly dependent stationary random matrices is derived doing away with the restriction of boundedness of the ratios of colum entries assumed by previous studies. Extensions beyond stationarity are discussed.     

Computability of the ergodic decomposition

The study of ergodic theorems from the viewpoint of computable analysis is a rich field of investigation. Interactions between algorithmic randomness, computability theory and ergodic theory have recently been examined by several authors. It has been observed that ergodic measures have better computability properties than non-ergodic ones. In a previous paper we studied the extent to which non-ergodic measures inherit the computability properties of ergodic ones, and introduced the notion of an effectively decomposable measure. We asked the following question: if the ergodic decomposition of a stationary measure is finite, is this decomposition effective? In this paper we answer the question in the negative.     

Maximal ergodic theorems for some group actions

We prove maximal ergodic inequalities for a sequence of operators and for their averages in the noncommutative Lp-space. We also obtain the corresponding individual ergodic theorems. Applying these results to actions of a free group on a von Neumann algebra, we get noncommutative analogues of maximal ergodic inequalities and pointwise ergodic theorems of Nevo-Stein.     

The large deviations theorem and ergodicity

In this paper, some relationships between stochastic and topological properties of dynamical systems are studied. For a continuous map f from a compact metric space X into itself, we show that if f satisfies the large deviations theorem then it is topologically ergodic. Moreover, we introduce the topologically strong ergodicity, and prove that if f is a topologically strongly ergodic map satisfying the large deviations theorem then it is sensitively dependent on initial conditions.     

遍历性及其应用──(Ⅰ)基本性质(英)

在一般意义下，给出了函数的遍历性定义．指出遍历函数是比概周期函数、渐近概周期函数及弱概周期函数更广的一类函数．文章讨论了遍历函数的一些性质，其中一个主要结果是给出了一个不等式的明确表达式．     

Wide sense regenerative processes with applications to multi-channel queues and networks

A general method for the analysis of queueing networks called regenerative decomposition is discussed. It includes global ergodic analysis of the whole network and a following detailed analysis of each separate node.In the first stage, ergodic conditions are deduced under which the processes describing the network and each node are regenerative (in a wide sense). In the paper, we concentrate mainly on the following stage of analysis (local analysis) which includes obtaining some rate conservation laws for the limiting distributions of the continuous time and (embedded) discrete time processes describing a separate nodes under ergodic conditions.Some useful properties of regenerative wide sense processes are considered in detail.     

A Banach space-valued ergodic theorem for amenable groups and applications

In this paper, we study unimodular amenable groups. The first part of the paper is devoted to results on the existence of uniform families of ε-quasi tilings for these groups. First we extend constructions of Ornstein and Weiss by quantitative estimates for the covering properties of the corresponding decompositions. Then we apply the methods developed to obtain an abstract ergodic theorem for a class of functions mapping subsets of a countable amenable group into some Banach space. This result extends significantly and complements related results found in the literature. Further, using the Lindenstrauss ergodic theorem, we link our results to classical ergodic theory. We conclude with two important applications: uniform approximation of the integrated density of states on amenable Cayley graphs and almost-sure convergence of cluster densities in an amenable bond percolation model.     

Ergodic properties of real cocycles and pseudo-homogeneous Banach spaces

Given an irrational rotation, in the space of real bounded variation functions it is proved that there are ergodic cocycles whose small perturbations remain ergodic; in fact, the set of ergodic cocycles has nonempty dense interior.

Given a pseudo-homogeneous Banach space and an irrational rotation, we study the set of elements satisfying the mean ergodic theorem. Once such a space is not homogeneous, we prove it is not reflexive and not separable. In ``natural" cases, up to -cohomology, the only elements satisfying the mean ergodic theorem are those from the closure of trigonometric polynomials.

For pseudo-homogeneous spaces admitting a Koksma's inequality ergodicity of the corresponding cylinder flows can be deduced from spectral properties of some circle extensions. In particular this is the case of Lebesgue spectrum (in the orthocomplement of the space of eigenfunctions) for the circle extension.

     

二重非齐次马氏链的遍历性及其应用

给出二重非齐次马氏链的强遍历性,绝对平均强遍历性,Cesaro平均收敛的概念．利用二维马氏链的遍历性和C-K方程,建立了二维马氏链与二重非齐次马氏链遍历性的关系．并讨论了齐次二重马氏链绝对平均强遍历与强遍历的等价性．最后给出Cesaro平均收敛在马氏决策过程和信息论中应用．