马尔可夫跳过程的弱收敛

本文通过马尔可夫跳过程的嵌入链的收敛性表征马尔可夫跳过程的弱收敛。特别,得到了用无穷小特征表征的时齐马尔可夫跳过程的收敛定理及时齐马尔可夫跳过程的离散逼近。     

带马尔可夫跳的随机Hopfield神经网络的以分布渐近稳定性

讨论了带马尔可夫跳的随机Hopfield神经网络的以分布渐近稳定性.通过构造合适的Lyapunov函数,获得了判定带马尔可夫跳的随机Hopfield神经网络的以分布渐近稳定性的充分条件.     

带马尔可夫跳的时滞随机递归神经网络的以分布渐近稳定性

研究了带马尔可夫跳的时滞随机递归神经网络的以分布渐近稳定性问题.通过构造合适的Lyapunov泛函,得到了判定带马尔可夫跳的时滞随机递归神经网络的以分布渐近稳定的充分条件.并举例说明结论的有效性.     

具脉冲混合时滞马尔可夫跳中立型随机神经网络系统指数稳定性

研究了具脉冲和混合时滞马尔可夫跳随机神经网络的鲁棒指数稳定性.通过构造合适Lyapunov-Krasovsii泛函,利用随机Lyapunov稳定性理论,给出并证明了该系统均方指数稳定性的充分条件,所有结果以线性矩阵不等式的形式给,数值算例表明无论脉冲是否发生在马尔可夫跳时刻,给出的稳定性标准都是有效的.     

马尔可夫调制及带Poisson跳随机时滞微分方程依分布稳定

本文讨论马尔可夫调制及带Poisson跳随机时滞微分方程,其主要目的是研究方程解的依分布稳定.     

Q过程唯一性的实用判别准则（英文）

首先简要介绍自1977年左右开始的寻找连续时间马尔可夫跳过程实用的唯一性充分条件的故事.对于一般状态空间的一般性结果是1985年得到的.为展示这些充分条件的精确性,于1991年找到非唯一性的对偶判别准则.本文主要限于离散空间(此时的跳过程也称为Q过程或马尔可夫链).在这种情况下,我们将在文末证明上述充分条件也是必要的.我们还将举例说明不论对于唯一性或非唯一性,我们的充分条件不仅强有力,而且精确.     

随机广义耦合微分Riccati方程解的存在性（英文）

本文研究利用奇异值分解方法,获得了随机广义耦合微分Riccati方程解的存在性.另外,作为应用,我们将解的存在性结论应用到了,带马尔可夫跳的线性随机奇异系统最优控制问题,并得到有限时区上的最优控制问题中最优控制的显式表示形式.     

拟对称Markov链泛函型中心极限定理

本文研究了一般的马尔可夫链特别是拟对称马尔可夫链．利用Lyons-Meyer-Zheng对称马尔可夫过程的鞅分解，建立了泛函型中心极限定理．推广到了一般平稳遍历马尔可夫过程。     

不确定半马尔可夫跳变系统的滑模观测器设计

考虑了相位型半马尔可夫跳变系统的滑模观测器设计问题.利用补充变量法及模型转化,将有限相位型半马尔可夫过程转换为其伴随马尔可夫链.因此,相位型半马尔可夫跳变系统可等价地转换为其伴随马尔可夫跳变系统.针对这类系统设计了滑模观测器并给出了观测器可解的充分条件.最后,通过数值算例表明了文章给出方法的有效性.     

拟对称马尔可夫过程穿越次数估计

本文研究了马尔可夫过程穿越次数估计问题.利用向前向后鞅分解方法,获得了拟对称马尔可夫过程的穿越次数估计,将Lyons-Zheng的马尔可夫过程的穿越次数估计从对称情形推广到拟对称情形.     

Stochastic Processes with Age-Dependent Transition Rates

We study stochastic processes with age-dependent transition rates. A typical example of such a process is a semi-Markov process which is completely determined by the holding time distributions in each state and the transition probabilities of the embedded Markov chain. The process we construct generalizes semi-Markov processes. One important feature of this process is that unlike semi-Markov processes the transition probabilities of this process are age-dependent. Under certain condition we establish the Feller property of the process. Finally, we compute the limiting distribution of the process.     

Stochastic analysis of transit systems

This paper presents two mathematical models representing on surface transit systems with general failure, towing and repair time distributions. The stochastic analysis is performed with the aid of the regeneration point technique. Laplace transforms of the state probabilities are obtained. A number of general formulas are developed for the transit system steady-state availability when one of the system transition rates is described by the Erlangian probability density function. Various plots of transit system steady-state availability are shown.     

Insensitivity of Generalized Semi-Markov Processes Evolving in a Random Environment

The theory of insensitivity within generalized semi-Markov processes is extended to cover the case where such a process evolves in a random environment; that is, when the decay rates and transition probabilities are functions of the state of an extraneous environmental process.     

Interactive markov chains

Markov chains, and various generalizations of them, almost universally assume that the transition probabilities applying to a single individual are independent of the behavior of other individuals in the population. That is, there is no interaction among individuals. This is an extremely limiting assumption in modelling social processes. This paper concerns interactive Markov chains, defined as Markov chains in which transition probabilities are functions of population frequencies in the states.     

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     

Random effects model for credit rating transitions

This paper proposes a random effects multinomial regression model to estimate transition probabilities of credit ratings. Unlike the previous studies on the rating transition, we applied a random effects model, which accommodates not only the environmental characteristics of the exposures of a rating but also the uncertainty not explained by such factors. The rating category specific factors such as retained earning and market equity are included in our proposed model. The random effects model provides less diagonally dominant matrix, where the transition probabilities are over-dispersed from the diagonal elements. Our study is expected to incorporate potential chances of rating transitions due to extra random variations.     

Perturbed Markov Chains with Damping Component

The paper is devoted to studies of regularly and singularly perturbed Markov chains with damping component. In such models, a matrix of transition probabilities is regularised by adding a special damping matrix multiplied by a small damping (perturbation) parameter ε. We perform a detailed perturbation analysis for such Markov chains, particularly, give effective upper bounds for the rate of approximation for stationary distributions of unperturbed Markov chains by stationary distributions of perturbed Markov chains with regularised matrices of transition probabilities, asymptotic expansions for approximating stationary distributions with respect to damping parameter, explicit coupling type upper bounds for the rate of convergence in ergodic theorems for n-step transition probabilities, as well as ergodic theorems in triangular array mode.

     

Exponential Ergodicity for SDEs with Jumps and Non-Lipschitz Coefficients

In this paper we show irreducibility and the strong Feller property for transition probabilities of stochastic differential equations with jumps and monotone coefficients. Thus, exponential ergodicity and the spectral gap for the corresponding transition semigroups are obtained.     

Birthing Markov processes at random rates

Summary This paper studies processes constructed by birthing the trajectories of a given Markov process along time according to random probabilities. Getoor has considered the case where the random probabilities are determined by comultiplicative functionals and proved for right processes that the post-birth process has the Markov property. Here randomizations of comultiplicative functionals are described which give rise to conditionally Markov processes. The main argument is developed for general Markov processes and the transition probabilities of the new process, including those from the pre-birth state, are explicited.