齐次可列马尔科夫链幂收敛性的注记

给出齐次可列马尔科夫键转移矩阵的一种置换相似标准型，并用之来讨论键的极限性态，分别明确给出转移矩阵益收敛于零矩阵、非零矩阵、随机矩阵、常随机矩阵和正的常随机矩阵的充分必要条件．     

Geometric Convergence Rates for Time-Sampled Markov Chains

We consider time-sampled Markov chain kernels, of the form P = _n n P ⁿ . We prove bounds on the total variation distance to stationarity of such chains. We are motivated by the analysis of near-periodic MCMC algorithms.     

关于非齐次马氏过程散度的极限性质

将数列上的绝对平均收敛性推广到平面上,并得出相应的引理.利用这个概念给出非齐次马氏过程散度率存在的一个条件.     

渐近循环马氏链的收敛速度

引入了渐近循环马氏链的概念,它是循环马氏链概念的推广.首先研究了在强遍历的条件下,可列循环马氏链的收敛速度,作为主要结论给出了当满足不同条件时可列渐近循环马氏链的C-强遍历性,一致C-强遍历性和一致C-强遍历的收敛速度     

依状态独立的随机环境中的马氏链

本主要讨论了依状态独立的随机环境中的马氏链，并严格地证明了依状态独立的随机环境中的马氏链，如果在环境不退化的一般情形下，不是时齐马氏链，而环境退化必然是马氏链这个结论。     

基于倾斜-t Copula的半参数马尔可夫链

在不指定时间序列结构的情况下,我们的分布模型是基于多变量离散时间的相应马尔可夫族和相关变量一维的边际分布.这样的模型可以同时处理时间序列之间的相互依赖和每个时间序列沿时间方向的依赖.具体的参数copula被指定为倾斜-t. 倾斜-t Copla能够处理不对称,偏斜和粗尾的数据分布.三个股票指数日均收益的实证研究表明,倾斜-t copula的马尔可夫模型要比以下模型更好:倾斜正态Copula马可夫, t-copula马可夫, 倾斜-t copula但无马尔可夫特性.     

双无限随机环境中的常返马氏链

对双无限随机环境中的马氏链,给出了常返的两种可能的定义,讨论了它们间的联系和基本性质,给出了状态或链为常返的判断准则.讨论了双无限随机环境中马氏链的不变测度的存在性,首次给出了双无限随机环境中马氏链的正常返及零常返的概念,并讨论了其相关性质.特别地,应用不变函数的性质,给出了状态具有正常返性或零常返性的判断准则.     

Singularly Perturbed Markov Chains: Convergence and Aggregation

Asymptotic properties of singularly perturbed Markov chains having measurable and/or continuous generators are developed in this work. The Markov chain under consideration has a finite-state space and is allowed to be nonstationary. Its generator consists of a rapidly varying part and a slowly changing part. The primary concerns are on the properties of the probability vectors and an aggregated process that depend on the characteristics of the fast varying part of the generators. The fast changing part of the generators can either consist of l recurrent classes, or include also transient states in addition to the recurrent classes. The case of inclusion of transient states is examined in detail. Convergence of the probability vectors under the weak topology of L² is obtained first. Then under slightly stronger conditions, it is shown that the convergence also takes place pointwise. Moreover, convergence under the norm topology of L² is derived. Furthermore, a process with aggregated states is obtained which converges to a Markov chain in distribution.     

Self-Interacting Markov Chains: Some Asymptotics

Abstract

Guided by the self-interaction mechanisms introduced in Benaim et al. [2 Benaim , M. , Ledoux , M. , and Raimond , O. 2002 . Self-interacting diffusions . Probab. Theory Related Fields 122 : 1 – 41 . [Google Scholar]] and in [5 Del Moral , P. , and Miclo , L. 2006 . Self-interacting Markov chains . Stochastic Anal. Appl. 24 : 615 – 660 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]], we present a more general definition of self-interacting Markov chains (SIMCs) (than in Del Moral and Miclo [5 Del Moral , P. , and Miclo , L. 2006 . Self-interacting Markov chains . Stochastic Anal. Appl. 24 : 615 – 660 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]] and Benaim et al. [2 Benaim , M. , Ledoux , M. , and Raimond , O. 2002 . Self-interacting diffusions . Probab. Theory Related Fields 122 : 1 – 41 . [Google Scholar]]). We then establish, for particular self-interaction mechanisms, a stability theorem with error estimation, two central limit theorems, two functional central limit theorems, and the large deviation principle.     

非齐次马尔可夫链的Gesaro—极限定理

本提出了新的非齐次马尔可夫链的遍历条件,并在此条件下,首次证明了非齐次马尔可夫链转移概率的Ｇｅｓａｒｏ－极限定理。另外,本还给出了一个例子,用它表明本的条件确实比Ｄｏｅｂｌｉｎ条件要弱。     

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.     

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本文研究了双无限环境中马氏链函数加权和的极限定理, 得到了双无限环境中马氏链函数加权和强收敛性成立的一系列充分条件.     

一个关于马尔可夫链的极限定理

给出一个关于可列非齐次马尔可夫链M元状态序组出现频率的新形式的强极限定理,所得结论对任意可列非齐次马尔可夫链普遍成立.     

关于马氏环境中马氏链的强极限定理的注

利用鞅收敛定理讨论马氏环境中马氏链的强收敛性,建立相应的强大数定律,使得已知的一系列结果为其特例.     

双无限随机环境中马氏链的暂留性

借鉴确定环境中马氏链暂留性的定义,在随机环境中马氏链的研究领域,引入了各种暂留性的概念,在确定环境中这些暂留性是等价的,而在随机环境中它们不等价.讨论了各类暂留性之间的相互关系及其基本性质,给出了链和状态是暂留的一些判别准则.     

Exponential Convergence Rates of Markov Chains under a Weaken Minorization Condition

In this paper, we obtain the quantitative bound of the exponential convergence rates of Markov chains under a weaken minorization condition, using the coupling method and the analytic approach. And also, we obtain the convergence rates for continuous time Markov processes.     

随机环境中马氏链的强常返性

讨论了随机环境中马氏链的强常返性,给出了在一类条件下,弱常返是强常返的及判定X是强常返的一个充分条件.     

马氏环境中的马氏链与马氏双链

本文研究了马氏环境中的马氏链,利用马氏双链的性质,得到了马氏环境中的马氏链回返于小柱集上的概率的若干估计式.     

随机有序马尔可夫链收敛速度显式界的注记

弱化Scott与Tweedie在计算马氏链收敛速度界时的条件,即变一步转移概率为m(m≥1)步转移概率,并运用不同于Scott与Tweedie的方法,计算出马氏链几何收敛速度r~n的界,从而推广了已有的结论.     

Quasi-Feller Extensions of Markov Chains and Existence of Dual Chains

The author presents a revised and detailed version of his theorem on the existence of Feller's extensions of Markov chains; to this end the broader notion of quasi-Feller extension is used. The existence of Markov chains dual to the chains with Borel space of states is derived from this result. Chains irreducible in the Orey sense are studied in most detail. For example, we prove that for such chains the quasi-Feller extension can be chosen recurrent or Liouville if the original chains possess these properties.