一类特殊的两性G -W分支过程及其谱半径

谱半径是不可约马尔可夫链的一个很重要的特征数字.本文主要介绍了两性G-W分支过程,并计算了一类特殊配对函数L(x,y)=x的两性G-W分支过程的谱半径.     

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.     

马尔可夫链的单点连通

给定一列离散时间马尔可夫链,我们构造它们的单点连通,即在各自的状态空间中取出一个状态视为一个状态,其它的状态保持原状,它们的相通必须通过这个合成的状态。证明了单点连通为不可约、常返、正常返的充要条件是每个分支链为不可约、常返、正常返。在非常返情形,得到了沿各个由零状态开始的分支趋于无穷的概率。由此提供了一个刻划非常返程度的度量。类似地构造了一列Q-矩阵的单点连通。证明了单点连通为规则Q-矩阵的充要条件是每个分支Q-矩阵为规则的。在规则情形也证明了单点连通Q-过程是不可约、常返、正常返的充要条件相应地是每个分支Q-过程是不可约、常返、正常返的。     

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.     

独立同分布随机环境中两性Galton-Watson分支过程灭绝概率的渐近行为

本文研究了独立同分布随机环境中的两性Galton-Watson分支过程,在上临界情形下,当k充分大时,qk≤ck<'-α>.     

具有马尔可夫增量的随机游动的最小值的局部极限定理（英文）

本文考虑具有马尔可夫增量的随机游动(半马尔可夫链)的最小值,提出一种Presman因式分解的方法,对其分布的渐进行为进行研究并给出了局部极限定理.该结果可以应用于对马尔可夫随机环境下的分支过程的生存概率的渐进行为进行估计.     

连续时间马氏链中拟平稳分布和不变分布之间的关系

Van Doorn(1991)说明了一个有吸收态的生灭过程中,如何有过程的转移概率来确定拟平衡分布,Nair和Pollett(1933)把它推广到由一个不可约类C和一个吸收态0。并且0从可可到不可约类C的连续时间马氏链,本对一个连续时间马氏连讨论了拟平稳分布与不变分布之间的关系。     

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．     

关于逆N0-矩阵的若干性质

1989年Meyer为计算马尔可夫链的平稳分布向量构造了一个算法,首次提出非负不可约矩阵的Perron补的概念.在非负不可约矩阵的广义Perron补若干性质的基础上,给出逆N0-矩阵的几个性质.     

关于逆N0-矩阵的若干性质

1989年Meyer为计算马尔可夫链的平稳分布向量构造了一个算法,首次提出非负不可约矩阵的Perron补的概念.在非负不可约矩阵的广义Perron补若干性质的基础上,给出逆N0-矩阵的几个性质.     

SPECTRAL RADIUSES OF THE GALTON-WATSON BRANCHING PROCESSES

§1IntroductionSuppose that(X,Px)is a Markov chain on a countable(or finite)state space E.Givenany x,y∈E,we say that y can be reached from x and write x y,if there is n≥1suchthat Px(Xn=y)>0.If x y and y z,then x z.The markov chain X is said to beirreducible if any two states can be reached from each other.(See[1]or[2]).If X isirreducible,then there is a number r,with0≤r≤1,such that lim supn→∞[Px(Xn=y)]n1=r forany x,y∈E.The number r is called the spectral radius of X(refer to[3]).…     

Galton-Watson分支过程的谱半径

The spectral radiuses of Galton-Watson branching processes which describes the speed of the process escaping from any state are calculated.Under the condition of irreducibility,it is show that this is equal to the spectral radius of Jacobi matrix of its generating function.     

On regular branching processes with infinite mean

A martingale, previously used to prove the classical almost sure convergence of the normed supercritical Galton-Watson branching process with finite mean without using probability generating functions, is here used to study similar behaviour for certain processes with infinite mean.     

Ruin Probabilities in Cox Risk Models with Two Dependent Classes of Business

In this paper we consider risk processes with two classes of business in which the two claim-number processes are dependent Cox processes. We first assume that the two claim-number processes have a two-dimensional Markovian intensity. Under this assumption, we not only study the sum of the two individual risk processes but also investigate the two-dimensional risk process formed by considering the two individual processes separately. For each of the two risk processes we derive an expression for the ruin probability, and then construct an upper bound for the ruin probability. We next assume that the intensity of the two claim-number processes follows a Markov chain. In this case, we examine the ruin probability of the sum of the two individual risk processes. Specifically, a differential system for the ruin probability is derived and numerical results are obtained for exponential claim sizes.     

Convergence of critical multitype Galton-Watson branching processes

Allowing an offspring probability distribution that has infinite variances, we establish the convergence in finite-dimensional distributions of normalized critical multitype Galton-Watson branching processes with increasing initial population size in the two cases of not conditioning and of conditioning on non-extinction of the processes in the nth generation. Furthermore, if the offspring probability distribution has only finite variances, we show that some linear functions of the above processes weakly converge to the diffusions given by Feller, and by Lamperti and Ney.     

Bisexual Galton-Watson Branching Processes in Random Environments

In this paper, we consider a bisexual Galton-Watson branching process whose offspring probability distribution is controlled by a random environment proccss. Some results for the probability generating functions associated with the process are obtained and sufficient conditions for certain extinction and for non-certain extinction are established.     

On the spectrum of Markov semigroups via sample path large deviations

The essential spectral radius of a sub-Markovian process is defined as the infimum of the spectral radiuses of all local perturbations of the process. When the family of rescaled processes satisfies sample path large deviation principle, the spectral radius and the essential spectral radius are expressed in terms of the rate function. The paper is motivated by applications to reflected diffusions and jump Markov processes describing stochastic networks for which the sample path large deviation principle has been established and the rate function has been identified while essential spectral radius has not been calculated.