非齐次马尔可夫链的Gesaro—极限定理

本提出了新的非齐次马尔可夫链的遍历条件，并在此条件下，首次证明了非齐次马尔可夫链转移概率的Ｇｅｓａｒｏ－极限定理。另外，本还给出了一个例子，用它表明本的条件确实比Ｄｏｅｂｌｉｎ条件要弱。     

带有缓冲器串行生产线的Harris链结构分析

本文以随机过程中的一类特殊的Ｍａｒｋｏｖ链（Ｈａｒｒｉｓ常返Ｍａｒｋｏｖ链）为工具，研究离散事件动态系统（ＤＥＤＳ）中的典型情况之一：带有缓冲器的串行生产线．求得了各缓冲器中产品数的联合稳态分布，产品在各台机器上受阻时间的联合稳态分布，以及受阻时间的强大数定律和产品在各台机器加工完时刻的极限行为．     

N参数Ornstein-Uhlenbeck过程的点常返性

本文得到了Ｎ参数 Ｏｒｎｓｔｅｉｎ－Ｕｈｌｅｎｂｅｃｋ过程的点常返性准则，我们证明了：若 ｄ＜ ２Ｎ，则ｄ－维 ＯＵＰＮ，Ｘｚ是点常返的；若 ｄ ≥２Ｎ，则Ｘｚ以概率 １不击中点。     

直线上的独立随机环境中可逗留的随机游动

主要讨论直线上独立随机环境中可逗留的随机游动的常返性和非常返性,并进一步研究常返性中的正常返和零常返.     

半直线上随机环境中可逗留随机游动的常返性

本文主要讨论了在独立但不同分布环境下，半直线上可逗留随机环境中随机游动的常返性和非常返性，并进一步研究了常返性中的正常返性和零常返性．     

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。     

跳过程μ正则性和不变测度存在性

本文给出了一般状态跳过程μ正则的充分条件,作为其推论得到跳跃链常返的跳过程是μ正则的,证明了跳跃链常返的跳过程,其q对的不变测度是跳过程的不变测度.还证明了跳跃链常返的跳过程存在唯一的不变测度.     

随机环境中马氏链的强常返性

讨论了随机环境中马氏链的强常返性,给出了在一类条件下,弱常返是强常返的及判定X是强常返的一个充分条件.     

RWdn的常返性

设X={X(z),z∈Tn}是文献[1]中定义的n参数d维随机游动(RWdn),本文主要研究RWdn的常返性,得到了关于RWdn的常返性的一些判别准则,并举例说明了几种RWdn的常返性.     

关于一般马尔可夫过程轨道常返性及暂留性

本文讨论了一般马尔可夫过程轨道常返性及暂留性，得到了一般马尔可夫过程轨道点常返及区域常返的一些判别准则。     

Strong 0-discount optimal policies in a Markov decision process with a Borel state space

We consider a Markov decision process with a Borel state space, a countable action space, finite action sets, bounded rewards and a bounded transition density satisfying a simultaneous Doeblin condition. The existence of stationary strong 0-discount optimal polices is proved.Supported by NSF grant DMS-9404177.     

Optimal Control Problem for the Lyapunov Exponents of Random Matrix Products

This paper deals with the optimal control problem for the Lyapunov exponents of stochastic matrix products when these matrices depend on a controlled Markov process with values in a finite or countable set. Under some hypotheses, the reduced process satisfies the Doeblin condition and the existence of an optimal control is proved. Furthermore, with this optimal control, the spectrum of the system consists of only one element.     

随机环境中的马氏链的不变测度与遍历性

本文考虑了一类特殊的随机环境的马氏链。假设随机“Doeblin”条件成立，我们证明了随机环境的马氏链的不变测度存在，且任何初始分布以指数收敛速度到些不变测度。进一步的，存在关于绕积算子遍历的不变测度。最后，我们得到了随机马氏链的强大数定律。     

Constrained markov decision processes with compact state and action spaces: the average case

Constrained Markov decision processes with compact state and action spaces are studied under long-run average reward or cost criteria. By introducing a corresponding Lagrange function, a saddle-point theorem is given, by which the existence of a constrained optimal pair of initial state distribution and policy is shown. Also, under the hypothesis of Doeblin, the functional characterization of a constrained optimal policy is obtained     

关于一类遗传算法收敛速度的研究

遗传算法收敛速度的研究是进化计算领域中一个复杂而重要的问题,但是有关收敛速度的研究结果还相对较少．目前有关遗传算法的收敛速度的结果可分为两类,一类是利用Doeblin条件来估计,但其结论中含有需要进一步估计的常量;另一类是利用状态转移矩阵的特征值来估计,然而同样需要进一步恰当地估计特征值的大小．本文首先给出一类遗传算法的框架,讨论了其全局收敛性,并且利用马尔可夫链的性质,估计了这类遗传算法的收敛速度．     

Optimality equations and inequalities in a class of risk-sensitive average cost Markov decision chains

This note concerns controlled Markov chains on a denumerable sate space. The performance of a control policy is measured by the risk-sensitive average criterion, and it is assumed that (a) the simultaneous Doeblin condition holds, and (b) the system is communicating under the action of each stationary policy. If the cost function is bounded below, it is established that the optimal average cost is characterized by an optimality inequality, and it is to shown that, even for bounded costs, such an inequality may be strict at every state. Also, for a nonnegative cost function with compact support, the existence an uniqueness of bounded solutions of the optimality equation is proved, and an example is provided to show that such a conclusion generally fails when the cost is negative at some state.     

Moderate deviations and functional limits for random processes with stationary and independent increments

We first give a functional moderate deviation principle for random processes with stationary and independent increments under the Ledoux's condition. Then we apply the result to the functional limits for increments of the processes and obtain some Csorgo-Revesz type functional laws of the iterated logarithm.     

Doeblin's big limit theorem

Doeblin regarded his paper(²) as his hardest work. The big limit is that ofP(ⁿ)(x, E) asn tends to infinity, in a measurable non-topologized space. An exposition of part one of this paper was published in Ref. 1. This is the exposition of part two, which contains some reparation as well as clarification.Doeblin's great contributions to probability theory were remembered at a conference 50 Years after Doeblin: Developments in the Theory of Markov Chains, Markov Processes and Sums of Random Variables held at Blaubeuren. Germany November 2–7, 1991. Professor Chung contributed this article to further celebrate this occasion. The editor thanks him.     

Quantitative Recurrence and Large Deviations for Teichmuller Geodesic Flow

We prove quantitative recurrence and large deviations results for the Teichmuller geodesic flow on connected components of strata of the moduli space Q _g of holomorphic unit-area quadratic differentials on a compact genus g ≥ 2 surface.     

Some Notes on Large Deviations of Markov Processes

In this paper we shall characterize the large deviation principles (abbreviated to LDP) of Donsker-Varadhan of a Markov process both for the weak convergence topology and for the τ-topology, by means of a hyper-exponential recurrence property. A Lyapunov criterion for this type of recurrence property is presented. These results are applied to countable Markov chains, unidimensional diffusions, elliptic or hypoelliptic diffusions on Rienmannian manifolds. Several counter-examples are equally presented. Received July 20, 1998, Accepted March 25, 1999