PageRank的改进算法——调整阻尼因子

Google将PageRank定义成某个非周期不可约Markov转移概率矩阵的平稳分布,于是对PageRank算法的改进所得到的矩阵一定要是非周期不可约Markov转移概率矩阵,结合RageRank算法和林共进修正算法思想,以及修正算法存在的问题,本文给出了改进算法,并通过简单试验对改进算法进行调整,调整后的改进算既满足Google的初衷又解决其算法的问题,也没有增加算法的复杂度.     

不同元件构成系统中元件维修率分布确定

将Markov链引入SFT理论中,计算可表示环境因素影响的元件维修率分布.研究针对不同元件构成的串联、并联和混联系统中元件的维修率分布计算方法.给出了串联和并联系统中元件维修率推导过程.对状态转移概率的计算不使用Markov状态转移矩阵求解,而是根据Markov状态转移图中的状态关系求解.使用SFT中的元件故障概率分布代替Markov链中的失效率,可得到元件维修率分布.以混联系统作为实例进行分析,使用状态关系求解各状态转移概率关系,得到了3个元件在使用时间t和使用温度c影响下的维修率分布,及正常状态转移概率范围.     

中国农村经济结构转移的Markov链研究

本文利用 Markov过程模型 ,对我国农村经济结构的变迁进行模拟与研究 .文中完成了各系统与子系统 Markov转移概率的估计 ,并以此为基础进行了统计分析与预测     

Markov链在生态学中的一个应用

Markov链是随机过程的一个特例,专门研究在无后效条件下时间和状态均为离散的随机转移问题.本文运用与Markov链相关的转移概率矩阵性质,探讨一个鱼类洄游实际问题的数学模型,寻求鱼类洄游的数量规律.     

BMAP的轨道分析和Q过程的伴随MAP

本文用轨道分析方法研究批量Markov到达过程(BMAP),有别于研究BMAP常用的矩阵解析方法.通过BMAP的表现(D_k,k=0,1,2,…),得到BMAP的跳跃概率,证明了BMAP的相过程是时间齐次Markov链,求出了相过程的转移概率和密度矩阵.此外,给定一个带有限状态空间的Q过程J,其跳跃点的计数过程记为N,证明了Q过程J的伴随过程X*=(N,J)是一个MAP,求出了该MAP的转移概率和表现(D_0,D_1),它们是通过密度矩阵Q来表述的.     

单个生产商和多个零售商缺货概率的计算法

由于需求的不确定性,容易造成缺货,如何计算缺货概率却是一个棘手的问题.本文把由单个制造商和多个零售商构成的供应链模型成Markov过程,利用排队理论分析供应链上各状态间的转移关系,以单个制造商和三个零售商为例澄清状态转移矩阵的内部结构,并对一般模型提出计算缺货和满货概率的计算公式.在此基础上分析了各状态概率对库存总成本的影响,为系统的优化决策提供分析的依据.数值实验表明所提出的方法是行之有效的.     

通过消息监控识别罪犯的Markov模型

通过消息监控识别罪犯是一个十分有意义的实际问题。本文采用Markov模型的方法,将整个消息传递网络看作一个犯罪传递的Markov链.根据所收集到的消息估计出两个节点（人）之间犯罪传递的概率,得到一个Markov概率转移矩阵,并求出网络长期运行下去的稳定解,作为各节点（人）参与犯罪程度的度量。文章通过实例说明该方法的有效性。     

中国股市一期价格行为研究

本文运用 CJ统计量与一步 Markov转移概率矩阵研究了中国沪、深两市的一期价格行为 .实证结果表明 :大约自 1997年以来 ,一期价格行为表现出很强的随机性 .     

多重休假的Bernoulli反馈M/G/1排队系统的稳态队长

系统地研究了多重休假的Bernoulli反馈排队模型,采用嵌入Markov链的方法,给出系统的一步转移概率矩阵进而求得稳态队长分布,并对排队顾客数进行随机分解,得到附加队长的母函数.     

关于本科教育中教学评价的转移概率矩阵模型

研究了以转移概率矩阵评价教学效果的两种方法:Markov链模型和罚因子法;特别是在第二种方法中,通过一个非常简单的"罚因子",可以迅速得到结论.利用这两种方法,有效的提高了教学评估的科学性,并且将这两种方法的适用范围加以推广.     

An algorithmic approach for a special class of Markov chains

In this paper, we develop an algorithmic method for the evaluation of the steady state probability vector of a special class of finite state Markov chains. For the class of Markov chains considered here, it is assumed that the matrix associated with the set of linear equations for the steady state probabilities possess a special structure, such that it can be rearranged and decomposed as a sum of two matrices, one lower triangular with nonzero diagonal elements, and the other an upper triangular matrix with only very few nonzero columns. Almost all Markov chain models of queueing systems with finite source and/or finite capacity and first-come-first-served or head of the line nonpreemptive priority service discipline belongs to this special class.     

Robustness and applicability of Markov chain Monte Carlo algorithms for eigenvalue problems

In this paper we analyse applicability and robustness of Markov chain Monte Carlo algorithms for eigenvalue problems. We restrict our consideration to real symmetric matrices.

Almost Optimal Monte Carlo (MAO) algorithms for solving eigenvalue problems are formulated. Results for the structure of both – systematic and probability error are presented. It is shown that the values of both errors can be controlled independently by different algorithmic parameters. The results present how the systematic error depends on the matrix spectrum. The analysis of the probability error is presented. It shows that the close (in some sense) the matrix under consideration is to the stochastic matrix the smaller is this error. Sufficient conditions for constructing robust and interpolation Monte Carlo algorithms are obtained. For stochastic matrices an interpolation Monte Carlo algorithm is constructed.

A number of numerical tests for large symmetric dense matrices are performed in order to study experimentally the dependence of the systematic error from the structure of matrix spectrum. We also study how the probability error depends on the balancing of the matrix.     

Comparison of subdominant eigenvalues of some linear search schemes

The subdominant eigenvalue of the transition probability matrix of a Markov chain is a determining factor in the speed of transition of the chain to a stationary state. However, these eigenvalues can be difficult to estimate in a theoretical sense. In this paper we revisit the problem of dynamically organizing a linear list. Items in the list are selected with certain unknown probabilities and then returned to the list according to one of two schemes: the move-to-front scheme or the transposition scheme. The eigenvalues of the transition probability matrix Q of the former scheme are well-known but those of the latter T are not. Nevertheless the transposition scheme gives rise to a reversible Markov chain. This enables us to employ a generalized Rayleigh-Ritz theorem to show that the subdominant eigenvalue of T is at least as large as the subdominant eigenvalue of Q.     

基于单重工作休假的离散时间排队稳态分析

详细地分析了一个单重工作休假的离散时间Geom/G/1排队系统.首先,构造二维嵌入马尔可夫链,得到其M/G/1型转移概率矩阵.其次,利用矩阵分析的方法,导出了稳态队长的概率分布,进一步得到稳态队长的随机分解结果和平均队长公式.最后,给出稳态等待时间的随机分解结构及其平均等待时间公式.     

基于马尔可夫模型的我国东、中、西部的产业结构预测

应用马尔可夫预测方法对我国东、中、西部产业结构预测问题进行研究,并给出了其马尔可夫的状态转移概率矩阵的估算模型,经计算结果表明此方法具有较高的预测精度,并应用此方法预测了我国2009年和2010年的东、中、西部的产业结构.     

Estimation in the Markov random walk scheme

The Markov random walk scheme is used to construct unbiased estimators for the function of the unknown transition probability matrix. Uniqueness of these estimators is investigated. Easily testable completeness conditions for Markov random walk plans are given.Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 35–54, 1986.     

Markov chain models for delinquency: Transition matrix estimation and forecasting

A Markov chain is a natural probability model for accounts receivable. For example, accounts that are ‘current’ this month have a probability of moving next month into ‘current’, ‘delinquent’ or ‘paid‐off’ states. If the transition matrix of the Markov chain were known, forecasts could be formed for future months for each state. This paper applies a Markov chain model to subprime loans that appear neither homogeneous nor stationary. Innovative estimation methods for the transition matrix are proposed. Bayes and empirical Bayes estimators are derived where the population is divided into segments or subpopulations whose transition matrices differ in some, but not all entries. Loan‐level models for key transition matrix entries can be constructed where loan‐level covariates capture the non‐stationarity of the transition matrix. Prediction is illustrated on a $7 billion portfolio of subprime fixed first mortgages and the forecasts show good agreement with actual balances in the delinquency states. Copyright © 2010 John Wiley & Sons, Ltd.