生灭型半马氏骨架过程

本文首先引进了生灭型半马氏骨架过程的定义,求出了两骨架时跳跃点τn-1(ω)与τn(ω)之间的嵌入过程X(n)(t,ω)的初始分布及寿命分布.得到了生灭型半马氏骨架过程的一维分布.其次引进了生灭型半马氏骨架过程的数字特征并讨论了它们的概率意义及相互关系.讨论了生灭型半马氏骨架过程的向上和向下的积分型随机泛函.最后讨论了它的遍历性及平稳分布,求出了平均首达时间及平均返回时间.得到了常返和正常返的充分必要条件,求出了在正常返的条件下的平稳分布.     

可修系统中半马氏过程的稳态分布

众所周知,可修系统是可靠性理论中讨论的一类非常重要的系统,也是可靠性数学主要研究对象之一,研究可修系统的主要数学工具是马氏理论.当构成系统各部件的寿命分布和故障后的修理时间分布,及其出现的有关分布均为指数分布时,只要适当的定义系统的状态,这样的系统总可以用马氏过程来描述.大部分学者为了方便,均是在马氏框架下研究问题的.但是在实践中经常遇到部件的寿命或修理时间分布不是指数分布的情形,这时可修系统所构成的随机过程是半马氏过程,用现有的马氏理论无法解决相关问题.目前,关于半马氏的理论研究的研究又很少,基于此,针对半马氏的随机模型给出了与马氏理论相平行的稳态分布的求解方法.     

半马氏生灭过程

本文提出了半马氏生灭过程的概念，引进了其数字特征，并讨论了向下和向上的积分型随机泛函、遍历性及平稳分布．     

非负费用折扣半马氏决策过程

本文考虑可数状态非负费用的折扣半马氏决策过程.首先在给定半马氏决策核和策略下构造一个连续时间半马氏决策过程,然后用最小非负解方法证明值函数满足最优方程和存在ε-最优平稳策略,并进一步给出最优策略的存在性条件及其一些性质.最后,给出了值迭代算法和一个数值算例.     

离散型冲击折扣半马氏决策过程

本文讨论离散型冲击折扣半马氏决策过程，在建立模型后，我们将它化成了一个等价的离散时间马氏决策过程．     

半马氏过程的积分型随机泛函

本文讨论了半马氏过程的积分型随机泛函,求出了“首达”时间的积分型随机泛函公式,并讨论了半马氏过程“正则性”条件,得到了飞跃点积分型随机泛函的两个0—1律     

盈余过程的马氏性与索赔到达间隔分布为离散型的连续时间风险模型

本文研究广泛的一类连续时间风险模型盈余过程的马氏性,得到了盈余过程成为马氏过程的充分必要条件．首次建立了索赔到达间隔为离散型分布的连续时间风险模型．并对两个基本特例得到了破产概率的准确表达式．     

马氏过程函数的强大数定律

本文主要研究了马氏过程函数以及马氏环境中马氏链函数的强大数定律．     

基于谱隙的依全变差指数式收敛速度估计

利用与谱隙作比较的手法，本文研究可逆马氏过程依全变差的指数式收敛速度．我们证明在相当一般的情况下，只要对初分布略加限制，则此速度以谱隙为下界．进而，对于紧空间情形或生灭过程或半直线上的扩散，我们证得此速度等于谱隙．     

马氏环境中马氏链的Poisson极限律

本文研究了马氏环境中马氏链,证明了该过程于小柱集上的回返次数是渐近地服从Poisson分布的,同时还给出了该过程是(?)-混合的一个充分条件以及过程回返于小柱集之概率的一个指数估计式.     

Semi-Markov failure rates processes

Usually, a reliability function is defined by a failure rate which is a real function taking the non-negative real values. In this paper the failure rate is assumed to be a stochastic process with non-negative and right continuous trajectories. The reliability function is defined as an expectation of a function of that random process. Particularly, the failure rate defined by the semi-Markov processes is considered here. The theorems dealing with the renewal equations for the conditional reliability functions with a semi-Markov process as a failure rate are presented in this paper. A system of that kind of equations for the discrete state space semi-Markov process is applied for calculating the reliability function for the 3-states semi-Markov random walk. Using the introduced system of renewal equations for the countable state space, the reliability function for the Furry-Yule failure rate process is obtained.     

Sufficient Stochastic Maximum Principle for the Optimal Control of Semi-Markov Modulated Jump-Diffusion with Application to Financial Optimization

The finite state semi-Markov process is a generalization over the Markov chain in which the sojourn time distribution is any general distribution. In this article, we provide a sufficient stochastic maximum principle for the optimal control of a semi-Markov modulated jump-diffusion process in which the drift, diffusion, and the jump kernel of the jump-diffusion process is modulated by a semi-Markov process. We also connect the sufficient stochastic maximum principle with the dynamic programming equation. We apply our results to finite horizon risk-sensitive control portfolio optimization problem and to a quadratic loss minimization problem.     

Ergodicity Conditions and Stationary Distributions of a Continuous Semi-Markov Process

A semi-Markov process of general type on a metric space is considered. The stationary distribution of the process is investigated. A Markov process associated with the semi-Markov one is constructed. The stationary distribution for values of the process at a fixed point of the time scale and for the lengths of intervals of constancy covering this point is expressed in terms of the stationary distribution of the associated Markov process. Bibliography: 11 titles.     

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.     

基于半马尔科夫过程的逻辑门可靠性分析

动态故障树分析方法是在静态故障树的基础上拓展而来的自上而下的图形化演绎技术,可以很好地对具有复杂失效行为和交互作用的系统进行建模,进而分析系统的可靠性。本文从动态故障树逻辑门的可靠性建模与分析入手,结合半马尔科夫过程原理,将动态逻辑门转化为半马尔科夫链。其次给出在半马尔科夫链中动态逻辑门输出事件的发生概率和系统可靠性的计算公式。提出各种逻辑门到半马尔科夫链的通用转化模型,通过更改通用模型中的相关参数,将逻辑门转化为半马尔科夫链。最后,基于半马尔科夫过程求解动态逻辑门输出事件的发生概率,以动态优先与门、顺序相关门和备件门为例,并给出系统可靠性的计算公式。     

Poisson Traffic Processes in RGSMP and Generalized Networks

1.Introductiontrafficprocessesinqueueingnetworksareanimportantoperatingfacetofsuchmodels,aswellasvaluableinthestudyofvaliddecompositionsofnetworks.IfwefindsometrafficprocessesinanetworkPoisson,thenitoftenrendersthemathematicalanalysistractable.Generalized…     

半马尔科夫下电场可修系统可靠性分析

众所周知,在马尔科夫模型下,在每个状态下的逗留时间服从指数分布,这经常太受限制,尤其是在电场可修系统中,不太适合操作数据要求.因此,提出了利用半马尔科夫过程去研究电场可修系统,而且,利用了马尔科夫更新理论和概率分析方法讨论了电场系统的稳态可用度.最后,通过一个数值例子陈述了获得的结果.     

An Algorithmic Approach to Discrete Time Non-homogeneous Backward Semi-Markov Reward Processes with an Application to Disability Insurance

In this paper semi-Markov reward models are presented. Higher moments of the reward process is presented for the first time applied to in time non-homogeneous semi-Markov insurance problems. Also an example is presented based on real disability data. Different algorithmic approaches to solve the problem is described. This work is partly supported by the Knowledge Foundation and Sparbankens Stiftelse Nya. The authors would like to thank the anonymous referee.     

Poisson Approximation of Impulsive Recurrent Process with Semi-Markov Switching

In this article, the weak convergence of impulsive recurrent process with semi-Markov switching in the scheme of Poisson approximation is proved. Singular perturbation problem for the compensating operator of the extended Markov renewal process is used to prove the relative compactness.     

Diffusion processes with delay at the endpoints of a segment

A continuous semi-Markov process with a segment as the range of values is considered. This process coincides with a diffusion process inside the segment, i.e., up to the first hitting time of the boundary of the segment and at any time when the process leaves the boundary. The class of such processes consists of Markov processes with reflection at the boundaries (instantaneously or with a delay) and semi-Markov processes with intervals of constancy on some boundary. We derive conditions of existence of such a process in terms of a semi-Markov transition generating function on the boundary. The method of imbedded alternating renewal processes is applied to find a stationary distribution of the process. Bibliography: 3 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 351, 2007, pp. 284–297.