THE CLASSIFICATION AND PERIOD OF STATES FOR MARKOV CHAIN IN RANDOM ENVIRONMENT

This paper is a continuation of [8]. In Section 1, three kinds of communication are introdnced for two states and the relations among them are investigated. In Section 2, two kinds of period of a state are introdnced and it is obtained that the period is a 'class property',i.e. two states x and y belong to same class implies the period of x is equal to the period of y.

ON MARKOV CHAINS IN SPACE-TIME RANDOM ENVIRONMENTS

In Section 1, the authors establish the models of two kinds of Markov chains in space-time random environments (MCSTRE and MCSTRE(+)) with abstract state space. In Section 2, the authors construct a MCSTRE and a MCSTRE(+) by an initial distribution Φ and a random Markov kernel (RMK) p(γ). In Section 3, the authors es-tablish several equivalence theorems on MCSTRE and MCSTRE(+). Finally, the authors give two very important examples of MCMSTRE, the random walk in spce-time random environment and the Markov br...

THE DECOMPOSITION OF STATE SPACE FOR MARKOV CHAIN IN RANDOM ENVIRONMENT

This paper is a continuation of [8] and [9]. The author obtains the decomposition of state space X of an Markov chain in random environment by making use of the results in [8] and [9], gives three examples, random walk in random environment, renewal process in random environment and queue process in random environment, and obtains the decompositions of the state spaces of these three special examples.

THE CONSTRUCTION OF MULTITYPE CANONICAL MARKOV BRANCHING CHAINS IN RANDOM ENVIRONMENTS

The investigation for branching processes has a long history by their strong physics background, but only a few authors have investigated the branching processes in random environments. First of all, the author introduces the concepts of the multitype canonical Markov branching chain in random environment （CMBCRE） and multitype Markov branching chain in random environment （MBCRE） and proved that CMBCRE must be MBCRE, and any MBCRE must be equivalent to another CMBCRE in distribution. The main results of this article are the construction of CMBCRE and some of its probability properties.

Model of Markov Chains in Space-Time Random Environments

A general framework of stochastic model for a Markov chain in a space-time random environment is introduced, here the environment ξ^＊：={ξ1,x∈N,x∈ X}is a random field. We study the dependence relations between the environment and the original chain, especially the ＂feedback＂. Some equivalence theorems and law of large numbers are obtained.

The Laplace Functional and Moments for Markov Branching Chains in Random Environments

The concepts of random Markov matrix, Markov branching chain in randomenvironment (MBCRE) and Laplace functional of Markov branching chain in random environment (LFMBCRE)are introduced. The properties of LFMBCRE and the explicit formulas of momentsof MBCRE are given.

The Classification of States for Markov Chain in Random Environments and m-irreducible

First of all, we introduces the concept of m-irreducible of Markov chain in random environment. Then under the condition of m-irreducible, the relationship of recurrent and positive recurrent between two states is studied. We also give several conditions that can imply a state is recurrent and positive recurrent. And then the period of a state is discussed and we obtained that under the condition of m-irreducible, for any two states in x, they have the same period.

The Relations Among Various Markov Chains

Some basic equations and the relations among various Markov chains are established. These works are the bases in the investigation of the theory of Markov chain in random environment.

STRONG LAW OF LARGE NUMBERS AND SHANNON-MCMILLAN THEOREM FOR MARKOV CHAINS FIELD ON CAYLEY TREE

This paper studies the strong law of large numbers and the Shannom-McMillan theorem for Markov chains field on Cayley tree. The authors first prove the strong law of large number on the frequencies of states and orderd couples of states for Markov chains field on Cayley tree. Then they prove the Shannon-McMillan theorem with a.e. convergence for Markov chains field on Cayley tree. In the proof, a new technique in the study the strong limit theorem in probability theory is applied.

POISSON LIMIT THEOREM FOR COUNTABLE MARKOV CHAINS IN MARKOVIAN ENVIRONMENTS

A countable Markov chain in a Markovian environment is considered.A Poisson limit theorem for the chain recurring to small cylindrical sets is mainly achieved.In order to prove this theorem,the entropy function h is introduced and the Shannon-McMillan-Breiman theorem for the Markov chain in a Markovian environment is shown. It's well-known that a Markov process in a Markovian environment is generally not a standard Markov chain,so an example of Poisson approximation for a process which is not a Markov process is given.On the other hand,when the environmental process degenerates to a constant sequence,a Poisson limit theorem for countable Markov chains,which is the generalization of Pitskel's result for finite Markov chains is obtained.

基于Markov链的变频调速系统随机PWM控制技术

将Markov链引入到传统随机脉宽调制(PWM)技术中,提出了一种基于Markov链的变频调速系统随机PWM技术。能够使随机周期值更均匀地分布在期望周期的周围,从而使输出电流频谱分布更加均匀、减小电机的电磁噪声和机械振动,而且与传统随机PWM相比,输出电流的纹波有明显的减小,提高了系统的控制性能。仿真和实验结果验证了算法的有效性。

黑河流域水资源动态变化及其趋势的灰色Markov链预测

根据有关水文气象台站的观测数据,对黑河流域水资源时空分布特征及变化规律进行了分析,并基于GM(1,1)模型和Markov链原理,提出了一个用于黑河流域的水资源变化趋势预测的灰色离散随机过程模型。结果表明,从1944年有观测记录以来的近60a时间里,以黑河干流为代表的黑河流域天然径流经历了几个长度不等的丰水段与枯水段,而目前正处于1996年开始第5个丰水段的下降段的最低点或自2000年开始的第6个枯水段的起始点。未来几年里,黑河流域天然水资源的变化总体上将呈现一种偏枯或平水偏枯的状态,但径流偏枯的幅度将不会很大。

区域交通网络行程时间估计的半Markov链模型

利用模糊聚类分析及典型判别方法,将区域交通网络单元路段的状态划分为3类,考虑到各类交通状态下拥挤效应的异同,对各状态下的瞬时行程时间函数进行了标定。然后,对区域交通网络的状态进行了定义,应用半Markov链随机过程理论,分析了给定时间段内某区域交通网络各种状态的随机变化规律,计算了各种状态出现的极限概率。最后,结合各状态下网络单元路段的瞬时行程时间函数,给出了给定时间段内的区域交通网络行程时间估计方法。将模型估计得到的行程时间与实测行程时间进行了对比,利用t检验法对估计结果进行了检验,检验结果表明,在显著性水平α=0.05的条件下,估计平均行程时间与实测行程时间均值没有显著性差异。

共和盆地天然草地牧草产量的Markov预测模型

Markov预测技术是应用Markov链的相关预测的基本原理与方法来研究分析时间序列的变化规律,并预测未来变化趋势的一种预报方法,适用于随机波动较大的预报问题。根据Markov链原理,提出了用于共和盆地温性草原类天然草地年平均牧草产量预报的离散随机过程模型。实测资料的验证结果表明,这种模型计算精度较高,具有良好的应用价值。

两种基于Markov链随机调制技术的比较研究

电力电子功率变换器中应用随机调制技术能有效地减小传导EN I,但会引起变换器输出电压纹波峰-峰值增加和精度降低,将M arkov链引入到随机调制技术中可有效地解决这个问题。由于M arkov链的状态选择对系统的运行性能和采用数控系统实现算法的实时性和快速性有着重要的影响,通过对两状态M arkov链和3状态M arkov链随机周期调制DC/DC变换器的仿真研究,结果表明3状态M arkov链随机周期调制技术具有更好的特性。

基于Markov链的三电平逆变器随机SVPWM控制方法

针对SVPWM调制中固定开关频率所引起的电磁污染问题,提出一种基于Markov链的随机SVPWM控制技术.通过Markov链得到逆变器的随机调制频率,与其他随机SVPWM调制方法相比,该调制频率在期望中心频率周围能够更加均匀地分布,输出电压频谱更加均匀且谐波畸变率有所减小,因此减小了系统的电磁干扰,改善了系统的电磁兼容性.基于SIMULINK的仿真实验验证了基于Markov链的随机SVPWM调制方法具有优越性.

Markov链的一种随机时间替换

研究Markov链的一种随机时间替换,这种替换有别于通常的Markov过程理论中的随机时间替换。通常的Markov过程的随机时间替换,是通过Markov过程的可加泛函来实现的。而现在,被随机时间替换的过程X={X(n),n=0,1,2…}是一个时间离散的、状态空间可数的、时间齐次的Markov链,用于随机时间替换的过程ι={ιt,t≥0}是一个时间连续的、状态空间为非负整数集的、不降的、空间齐次的Markov链,而且X与独立。证明了随机时间替换后的过程,Y={Y(t),t≥0},Y(t)=X(ιt)是一个Markov链;并求出了Y的转移概率;当是时间齐次时,Y也是时间齐次的。

基于Markov链的随机需求预测模型

随机需求预测是供应计划工作的重点和难点 ,应用马尔柯夫链分析法和蒙特卡洛仿真技术 ,可以建立一个有效实用的随机需求预测模型。

我国人均水资源量的灰色-加权Markov动态预测分析

引入灰精度指标,基于加权马尔可夫链理论对灰色模型进行改进,并以2000—2011年我国人均水资源量为基础,建立预测模型进行实证分析.结果表明,与传统的灰色预测相比,平均相对误差由15.94%降低为4.05%,较好地提高了预测的精度.

随机平稳策略下半Markov决策过程的仿真优化算法

基于性能势理论和等价Markov过程方法,研究了一类半Markov决策过程(SMDP)在参数化随机平稳策略下的仿真优化算法,并简要分析了算法的收敛性．通过SMDP的等价Markov过程,定义了一个一致化Markov链,然后根据该一致化Markov链的单个样本轨道来估计SMDP的平均代价性能指标关于策略参数的梯度,以寻找最优(或次优)策略．文中给出的算法是利用神经元网络来逼近参数化随机平稳策略,以节省计算机内存,避免了“维数灾”问题,适合于解决大状态空间系统的性能优化问题．最后给出了一个仿真实例来说明算法的应用．