高阶马尔可夫链的降阶模型及其应用

本文通过对传统高阶马尔可夫链模型的状态空间进行阶数重构,导出一个在重构状态空间上的降阶马尔可夫模型。理论分析证明,降阶马尔可夫链模型不但可以描述传统高阶马尔可夫链模型的全部性态,更能表达较传统模型细微的随机结构。然后,应用降阶模型对我国股票指数的动态变化进行实证分析,讨论了阶数的选取和高阶马尔可夫性检验,分析了股票市场内在波动结构。最后,对股指序列作出短期与长期的预测分析。     

马尔可夫链在技术创新成功率预测中的应用

马尔可夫链是研究复杂系统的一个数学模型,其预测的出发点是现有状态和当前条件,被认为是市场占有率、人才需求、设备更新等的较好预测模型.技术创新从新思想的产生到成功实现商业化,需要经过多个环节,受内外环境多个因素的影响,从而使得技术创新的风险性很高,这就需要对技术创新的成功概率进行预测,以降低风险.通过分析,技术创新链也符合马尔可夫过程,故依据技术创新程序和各阶段特点,构造技术创新马尔可夫链,并据此进一步构造出技术创新成功率预测模型.     

马尔可夫过程在医学干预措施成本效用分析中的应用

马尔可夫过程(Markov Process)是由一种状态转移至另一种状态的随机过程。本文探讨了医学干预措施成本效用分析中马尔可夫状态转移模型构建和模型参数的确定方法,并以全髋关节置换术为例,将具有吸收状态的离散马尔可夫过程应用于医学干预措施成本效用分析。结果表明,利用模型得出的预测结果与目前的医学认识和临床实际相符,提示应用离散马尔可夫过程预测医学干预措施成本效用是可行的。     

基于传导变换的马尔可夫链平稳分布的研究

利用可拓学中的参变量事元描述随机过程,引入了随机过程元的概念,建立了随机过程的可拓模型.利用随机事元刻画随机过程的状态,引入了随机状态元和随机状态元集的概念,给出了马尔可夫事元链模型.利用随机状态元的可拓性以及传导变换对马尔可夫链及其平稳分布进行了初步的拓展研究.     

基于改进的灰色马尔可夫链模型的交通事故预测

交通事故预测是交通安全评价、规划和决策的基础.灰色预测适合于数据量少和波动小的系统对象,而马尔可夫链理论适用于预测随机波动大的动态过程.为克服一般灰色马尔可夫链模型运用的转移概率矩阵固定不变而影响预测精度的问题,本文建立了改进的灰色马尔可夫链模型.采用滑动转移概率矩阵方法,去掉最老数据并补充最新数据,从而建立新的一步转移概率矩阵.借助改进的灰色马尔可夫链模型,对全国2002-2004年交通事故10万人口死亡率进行了预测分析.结果表明,改进的灰色马尔可夫链模型比一般灰色马尔可夫链模型的预测范围更准确,预测精度更高.     

马尔可夫骨架过程的有穷维分布(英文)

在文献[1]和[2]中，我们引入了马尔可夫骨架随机过程的概念，并得到了向后方程和向前方程．同时还计算了这类过程的一维分布以及讨论了其它有关性质．在本文中，我们进一步给出马尔可夫骨架随机过程的有穷维分布的计算公式．     

马尔可夫骨架PERT网络的最长路径

本文利用马尔可夫骨架过程理论研究PERT网络模型，其中网络各弧线的长度是相互独立的随机变量。文中构造了一个马尔可夫骨架过程，利用其向后方程求解随机网络最长路径长度的分布函数。     

画片组合中的概率问题

对于一个关于“抽奖资格”的概率问题，本文运用工程数学中概率论的有关知识进行了数学建模和解答，并进一步引入了随机过程和马尔可夫链的一些概念．     

基于灰色马尔可夫模型的物流配送需求量预测研究

研究可以较准确地预测物流配送需求量的数学模型,以服务于政府及企业的物流规划及其决策.将灰色理论和离散状态的马尔可夫链相结合,用灰色马尔可夫链对物流配送需求量进行实证研究.针对灰色数据系列首先用GM模型进行趋势预测,然后利用马尔可夫状态转移概率矩阵预报方法对其预测值进行二次拟合,预测精度明显高于GM模型预测.     

马尔可夫链模型在灾变预测中的应用

利用马尔可夫链模型的原理预测灾变，以郑州市旱涝等级的预测作为实例，介绍了使用这种模型的方法与步骤，预测结果表明，利用马尔可夫链模型预测灾变是可行的。     

Stability of a pure random delay system with two-time-scale Markovian switching

This work examines almost sure stability of a pure random delay system whose delay time is modeled by a finite state continuous-time Markov chain with two-time scales. The Markov chain contains a fast-varying part and a slowly-changing part. Using the properties of the weighted occupation measure of the Markov chain, it is shown that the overall system?s almost-sure-asymptotic stability can be obtained by using the “averaged” delay. This feature implies that even if some longer delay times may destabilize the system individually, the system may still be stable if their impact is balanced. In other words, the Markov chain becomes a stabilizing factor. Numerical results are provided to demonstrate our results.     

Pricing Derivatives under a Markov Skeleton Process

In this paper, it is assumed that the underlying is a Markov skeleton process (abbreviated MSP): this process can be better reflecting the instability of the financial market. Using the properties of Markov skeleton process, the characteristic function of the price process is given, combined with fast Fourier transform (FFT) method, the pricing formula of derivatives under the Markov skeleton process is given. The results of this paper can be applied to price other financial derivatives, and it enriching the pricing theory of financial derivatives.     

Large deviation principle of occupation measure for stochastic Burgers equation

In this paper we obtain a Large Deviation Principle for the occupation measure of the solution to a stochastic Burgers equation which describes the exact rate of exponential convergence. This Markov process is strongly Feller and has a unique invariant measure. Moreover, the rate function is explicit: it is the level-2 entropy of Donsker-Varadhan.     

The Geometric Markov Renewal Processes with Application to Finance

We introduce the geometric Markov renewal processes as a model for a security market and study this processes in a series scheme. We consider its approximations in the form of averaged, merged and double averaged geometric Markov renewal processes. Weak convergence analysis and rates of convergence of ergodic geometric Markov renewal processes are presented. Martingale properties, infinitesimal operators of geometric Markov renewal processes are presented and a Markov renewal equation for expectation is derived. As an application, we consider the case of two ergodic classes. Moreover, we consider a generalized binomial model for a security market induced by a position dependent random map as a special case of a geometric Markov renewal process.     

基于不同角色下的做市商制金融市场模型研究

本文建立了一类做市商制金融市场模型,在该模型中,做市商扮演了投资者和供应商的两种角色。通过利用离散动力系统的稳定性、分支理论,考虑了不动点的存在性,以及重要参数对系统稳定性的影响,尤其是做市商在角色转换中对系统稳定性的影响。得出通过适当调整库存调节速率,对防止市场价格的剧烈波动有一定的作用。     

Transient and Asymptotic Analysis of General Markov Fluid Models

In this paper, transient and asymptotic behaviors of general Markov fluid models are studied and analyzed. The input and output rates are assumed to be modulated by a finite state irreducible Markov process, which can admit states with zero effective input rate. The main advantage of the proposed methods is their accuracy and their numerical stability. For the transient solution, properties of stationary detection lead to reduce considerably the computational complexity of the algorithm. As for the asymptotic solution, it is derived from the transient one's. We apply these methods to a general Markov fluid model and we interpret the numerical results.     

Large Deviations for Empirical Measures of Not Necessarily Irreducible Countable Markov Chains with Arbitrary Initial Measures

All known results on large deviations of occupation measures of Markov processes are based on the assumption of （essential） irreducibility. In this paper we establish the weak＊ large deviation principle of occupation measures for any countable Markov chain with arbitrary initial measures. The new rate function that we obtain is not convex and depends on the initial measure, contrary to the （essentially） irreducible case.     

状态依赖下的股市正反馈交易

在Sentana和Wadhwani的正反馈模型基础上,本文利用前期涨跌进行状态划分,建立了正反馈交易的Markov状态依赖模型,考察市场中的正反馈交易行为与羊群效应。通过对中国股市的实证研究,可以发现,股价不服从随机游走,在前期股价连续上涨或下跌的情况下,转移概率具有惯性;中国股市存在显著的状态相依的正反馈行为,在前期股价连续上涨的情况下,易激发羊群行为。监管者应注重市场价格的持续变动,投资者可以采用正反馈交易策略。     

The impact of loyalty and promotion effects on retention rate

Researching customer retention rates is made difficult because of the lack of suitable systems with which to measure it. From a first-order Markov brand-switching model, serial equations are derived to estimate the retention rate using market share and loyalty. To explore the impact of loyalty and promotion programme on retention rate, data from five leading brands for three product categories were obtained to fit the developed model. Findings suggest that: (1) when the loyalty effect remains unchanged over a period of time, the greater the effect of a promotion programme, the greater the retention rate; (2) when the promotion effects among brands are similar, the retention rate varies depending on level of loyalty; and (3) when the proportion of loyal customers is high, the proportion of potential switchers affected by promotion programmes is low. In this case, the impact of a promotion programme on the retention rate is not significant. This model successfully demonstrates how the Markov brand-switching model can be employed to estimate a measure of retention rate from consumer panel data as well as to better understand how promotion affects loyalty, switching behaviour, and retention rate.