肖争艳等： 绕积马氏链的状态分类

该文给出了绕积马氏链的特征数和状态的定义, 利用一般马氏链的理论讨论了随机环 境中的马氏链的各种状态的特征以及各类状态之间的联系, 还给出了在联合空间不可分解且 正则本质的条件下, 状态正则本质的充要条件. 最后举例说明了经典马氏链和随机环境中马氏链的状态的区别.     

从p-m链到随机环境中的马氏链

第一节引进了p-m链的概念,并用之构造了与它相应的随机环境中的马氏链和绕积马氏链.第二节引进了一系列与随机环境中的马氏链相关的概率特性函数,并得到了这些函数之间的一系列关系.这些结果是经典马氏链的相应结果的一般化,它们在随机环境中的马氏链的极限理论的研究中是很有用的.     

从p—m链到随机环境中的马氏链

第一节引进了p一m链的概念,并用之构造了与它相应的随机环境中的马氏链和绕积马氏链、第二节引进了一系列与随机环境中的马氏链相关的概率特性函数,并得到了这些函数之间的一系列关系.这些结果是经典马氏链的相应结果的一般化,它们在随机环境中的马氏链的极限理论的研究中是很有用的。     

状态可数的马氏环境中马氏链函数的强大数定律

讨论了马氏双链与随机环境中马氏链的关系．在此基础上，研究了具有离散参量的马氏环境中马氏链函数的强大数定律，并且给出了直接加于链和过程样本函数上的充分条件．     

绕积马氏链的几个结果

本文利用一般马氏链的理论讨论了随机环境中的马氏链的各种状态的特征及遍历性,并用两种方式将状态空间进行严格的分类.     

随机环境中马氏链的强大数定律

本文研究随机环境中马氏链函数的极限定律，得到一类马氏环境中马氏链函数的强大数定律成立的充分条件．     

马氏环境中马氏链的Shannon-McMillan-Breiman定理

本文给出了随机环境中的可数状态马氏链的Ｓｈａｎｎｏｎ－ＭｃＭｉｌｌａｎ－Ｂｒｅｉｍａｎ定理,这自然是熟知的有限状态时齐马氏链相应结果的拓广。     

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.     

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.     

随机环境中马氏链的周期性和常返性

研究了随机环境中马氏链的周期性,引入了随机环境中马氏链的正常返和零常返,利用状态的周期讨论了随机环境中马氏链的正常返性,给出了状态正常返的若干充分条件,从而推广了经典马氏链的相应结论.     

Random walks generated by affine mappings

This article is concerned with Markov chains on ^m constructed by randomly choosing an affine map at each stage, and then making the transition from the current point to its image under this map. The distribution of the random affine map can depend on the current point (i.e., state of the chain). Sufficient conditions are given under which this chain is ergodic.     

THE CONSTRUCTION OF MULTITYPE CANONICAL MARKOV BRANCHING CHAINS IN RANDOM ENVIRONMENTS

The investigation for branching processes has a long history by their strong physics background, but only a few authors have investigated the branching processes in random environments. First of all, the author introduces the concepts of the multitype canonical Markov branching chain in random environment (CMBCRE) and multitype Markov branching chain in random environment (MBCRE) and proved that CMBCRE must be MBCRE, and any MBCRE must be equivalent to another CMBCRE in distribution. The main results of this article are the construction of CMBCRE and some of its probability properties.     

Computing the Stationary Distribution of Absorbing Markov Chains with One Eigenvector of Diagonalizable Transition Matrices

An absorbing Markov chain is an important statistic model and widely used in algorithm modeling for many disciplines, such as digital image processing, network analysis and so on. In order to get the stationary distribution for such model, the inverse of the transition matrix usually needs to be calculated. However, it is still difficult and costly for large matrices. In this paper, for absorbing Markov chains with two absorbing states, we propose a simple method to compute the stationary distribution for models with diagonalizable transition matrices. With this approach, only an eigenvector with eigenvalue 1 needs to be calculated. We also use this method to derive probabilities of the gambler's ruin problem from a matrix perspective. And, it is able to handle expansions of this problem. In fact, this approach is a variant of the general method for absorbing Markov chains. Similar techniques can be used to avoid calculating the inverse matrix in the general method.     

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??An absorbing Markov chain is an important statistic model and widely used in algorithm modeling for many disciplines, such as digital image processing, network analysis and so on. In order to get the stationary distribution for such model, the inverse of the transition matrix usually needs to be calculated. However, it is still difficult and costly for large matrices. In this paper, for absorbing Markov chains with two absorbing states, we propose a simple method to compute the stationary distribution for models with diagonalizable transition matrices. With this approach, only an eigenvector with eigenvalue 1 needs to be calculated. We also use this method to derive probabilities of the gambler's ruin problem from a matrix perspective. And, it is able to handle expansions of this problem. In fact, this approach is a variant of the general method for absorbing Markov chains. Similar techniques can be used to avoid calculating the inverse matrix in the general method.     

ON MARKOV CHAINS IN SPACE-TIME RANDOM ENVIRONMENTS

In Section 1, the authors establish the models of two kinds of Markov chains in space-time random environments (MCSTRE and MCSTRE(+)) with abstract state space. In Section 2, the authors construct a MCSTRE and a MCSTRE(+) by an initial distribution Φ and a random Markov kernel (RMK) p(γ). In Section 3, the authors es-tablish several equivalence theorems on MCSTRE and MCSTRE(+). Finally, the authors give two very important examples of MCMSTRE, the random walk in spce-time random environment and the Markov br...     

Quasi-stationary Distributions for a Class of Discrete-time Markov Chains

This paper is concerned with the circumstances under which a discrete-time absorbing Markov chain has a quasi-stationary distribution. We showed in a previous paper that a pure birth-death process with an absorbing bottom state has a quasi-stationary distribution—actually an infinite family of quasi-stationary distributions— if and only if absorption is certain and the chain is geometrically transient. If we widen the setting by allowing absorption in one step (killing) from any state, the two conditions are still necessary, but no longer sufficient. We show that the birth–death-type of behaviour prevails as long as the number of states in which killing can occur is finite. But if there are infinitely many such states, and if the chain is geometrically transient and absorption certain, then there may be 0, 1, or infinitely many quasi-stationary distributions. Examples of each type of behaviour are presented. We also survey and supplement the theory of quasi-stationary distributions for discrete-time Markov chains in general.      

DISRUPTION MANAGEMENT FOR SUPPLY CHAIN COORDINATION WITH EXPONENTIAL DEMAND FUNCTION

The coordination problem of a supply chain comprising one supplier and one retailer under market demand disruption is studied in this article. A novel exponential demand function is adopted, and the penalty cost is introduced explicitly to capture the deviation production cost caused by the market demand disruption. The optimal strategies are obtained for different disruption scale under the centralized mode. For the decentralized mode, it is proved that the supply chain can be fully coordinated by adjusting the price discount policy appropriately when disruption occurs. Furthermore, the authors point out that similar results can be established for more general demand functions that represent different market circumstances if certain assumptions are satisfied.     

Choosing a random spanning subtree: a case study

Broder⁽⁴⁾ has suggested a stochastic algorithm for generating a random spanning subtree of a graph. This paper studies this algorithm for a special class of graphs. A complete spectral decomposition of the associated Markov chain is given. The analysis available from this is compared to stopping-time techniques and purely geometric bounds on the second eigenvalue.     

The branching chain with drift in space-time random environment (I): Model,Markov property,moments

There are three parts in this article. In Section 1, we establish the model of branching chain with drift in space-time random environment (BCDSTRE), i.e., the coupling of branching chain and random walk. In Section 2, we prove that any BCDSTRE must be a Markov chain in time random environment when we consider the distribution of the particles in space as a random element. In Section 3, we calculate the first-order moments and the second-order moments of BCDSTRE.     

The coalescent

The n-coalescent is a continuous-time Markov chain on a finite set of states, which describes the family relationships among a sample of n members drawn from a large haploid population. Its transition probabilities can be calculated from a factorization of the chain into two independent components, a pure death process and a discrete-time jump chain. For a deeper study, it is useful to construct a more complicated Markov process in which n-coalescents for all values of n are embedded in a natural way.