非时齐马氏过程的对数Sobolev不等式

本文将时齐马氏过程的经典对数Sobolev不等式推广到非时齐马氏过程,建立了非时齐马氏过程的转移半群与对数Sobolev不等式之间的关系.     

非时齐马氏过程的Liggett-Stroock不等式

本文将时齐马氏过程中重要的代数不等式Liggett-Stroock不等式推广到非时齐马氏过程中,建立了非时齐马氏过程的转移半群与Liggett-Stroock不等式之间的关系.     

用概率距离研究非时齐马氏链的收敛性

该文用概率距离和耦合方法研究了一般状态空间非时齐马氏链的收敛性,得到了一般状态空间.非时齐马氏链收敛的一个条件.     

非时齐马氏过程的耦合基本定理

本文将耦合方法应用于非时齐马氏过程,推广了时齐情形的耦合基本定理,为后续研究非时齐马氏过程的耦合提供了理论基础.     

一个非时齐马氏过程

<正> 本文研究了一个非时齐马氏过程,考虑其瞬时性质与渐近性质.过程的实际背景是成批到来无限束的 M(t)/M(t)/∞排队问题,排队过程的到来的强度,批量的大小与服务的强度均随时间变化.§1.引言由于实践范围的扩大,若干重要马氏过程的非时齐情况在近年来都得到深入研究.本文旨在考虑一个出现于排队论中的非时齐马氏过程 (在排队论中非时齐过程的重要性早已在[2]中指出过).     

无界报酬非时齐折扣马氏决策模型

在文献[1]—[3]中在各自的条件下,讨论过非时齐折扣马氏决策模型及其ε(≥0)最优策略存在的条件.在文献[4],文献[5]中,在状态和行动集都是可数的条件下,讨论了具有绝对平均相对有界的无界报酬的时齐折扣马氏决策模型.本文在状态集仍为可数,行动集为任意的条件下,建立与[4]相应的非时齐的折扣马氏决策模型;给出模型的有限阶段逼近和建立最优方程;证明了ε(>0)最优马氏策略的存在性和行动集为有限集时最优     

连续时间非时齐马氏过程的广义Dobrushin系数的估计

本文研究了非时齐马氏过程的广义Dobrushin系数的估计问题.在将经典Dobrushin遍历系数推广为加权的遍历系数的基础上,利用了矩阵拆分的方法,得到了对这种广义遍历系数的估计方法,推广了时齐马氏过程关于遍历系数的估计结果,借此可进一步得到有关遍历性的判定结论.     

人寿保险中随机Thiele微分方程的另一方法及应用

本文针对人寿保单被描述为时间非时齐的马氏链情形,较之文[7]更一般的假设条件下,给出了鞅M(t)=E[V0│Ft]的局部平方可积鞅的表示性,该方法不同于文[4]的方法。由此得到了随机Thiele微分方程,而且给出损失方差的一般表示。文章最后通过赔偿依赖于准备金的寡妇养老 金例子说明了随机Thiele微分方程的应用。     

非时齐准转移函数及其所对应的两个单参数半群

众所周知，由于双参数半群的局限，使得对时齐马氏过程的许多结果无法在非时齐马氏过程得到，或得到的结果也较时齐的情况粗糙得多．本文给出了与非时齐准转移函数对应的两个单参数半群，研究了二者的性质，并证明了二者相互唯一决定。这就提供了一条由单参数压缩半群研究非时齐马氏过程的途径。     

Lévy型算子所生成马氏过程的稳定性

利用Levy型算子积分微分型表示形式和拟微分型表示形式,以寻求Levy型算子生成的马氏过程各种稳定性的精确且可验证的充分条件.给出了由符号函数直接判定的Levy型过程非爆炸的充分条件,这个条件包括了扩散过程非爆炸的线性增长条件;当Levy型算子生成马氏过程对应半群的符号函数已知时,得到了由该符号函数直接表达的常返性充分条件,它推广了关于Levy过程经典的Chung-Fuchs常返性准则.     

Recent Results on Recurrent Solutions and Limit Distributions of SDEs

The limit distribution for homogeneous Markov processes is studied extensively and well understood, but it is not the case for inhomogeneous Markov processes. In this paper, we review some recent results on inhomogeneous Markov processes generated by non-autonomous stochastic (partial) differential equations (SDE in short). Under some suitable conditions, we show that the distribution of recurrent solutions of SDEs constitutes the limit distribution of the corresponding inhomogeneous Markov processes.     

Markov Decision Processes with Variance Minimization: A New Condition and Approach

Abstract

This article deals with the limiting average variance criterion for discrete-time Markov decision processes in Borel spaces. The costs may have neither upper nor lower bounds. We propose another set of conditions under which we prove the existence of a variance minimal policy in the class of average expected cost optimal stationary policies. Our conditions are weaker than those in the previous literature. Moreover, some sufficient conditions for the existence of a variance minimal policy are imposed on the primitive data of the model. In particular, the stochastic monotonicity condition in this paper has been first used to study the limiting average variance criterion. Also, the optimality inequality approach provided here is different from the “optimality equation approach” widely used in the previous literature. Finally, we use a controlled queueing system to illustrate our results.     

$\boldsymbol{\mathcal{G}-}$Inhomogeneous Markov Systems of High Order

In the present, we introduce and study the G-\mathcal{G-}inhomogeneous Markov system of high order, which is a more general in many respects stochastic process than the known inhomogeneous Markov system. We define the inhomogeneous superficial razor cut mixture transition distribution model extending for the homogeneous case the idea of the mixture transition model. With the introduction of the appropriate vector stochastic process and the establishment of relationships among them, we study the asymptotic behaviour of the G-\mathcal{G-}inhomogeneous Markov system of high order. In the form of two theorems, the asymptotic behaviour of the inherent G-\mathcal{G-}inhomogeneous Markov chain and the expected and relative expected population structure of the G-\mathcal{G-}inhomogeneous Markov system of high order, are provided under assumptions easily met in practice. Finally, we provide an illustration of the present results in a manpower system.     

On stochastic boundedness and stationary measures for Markov processes

In this report we relate the property of stochastic boundedness to the existence of stationary measures for arbitrary Markov processes on the positive real line. We further develop a sufficiency criterion for the independence of such measures from initial conditions. The results are then applied to the question of approximating the fixed point vector of an irreducible infinite stochastic matrix by the solutions of finite ones.     

Déviations modérées pour la moyennisation d'une EDS avec petite diffusion

We prove in this Note the moderate deviation principle (MDP) for the averaging principle of a stochastic differential equation (SDE) in a fast random environment, modelized by an exponentially ergodic Markov process independent of the Wiener process driving the SDE. The main tools will be the method of Puhalskii for exponential tightness and a MDP for inhomogeneous functionals of Markov processes established in [5].     

Markov chain-based degree distributions of evolving networks

In this paper, we study a class of stochastic processes, called evolving network Markov chains, in evolving networks. Our approach is to transform the degree distribution problem of an evolving network to a corresponding problem of evolving network Markov chains. We investigate the evolving network Markov chains, thereby obtaining some exact formulas as well as a precise criterion for determining whether the steady degree distribution of the evolving network is a power-law or not. With this new method, we finally obtain a rigorous, exact and unified solution of the steady degree distribution of the evolving network.     

Unreliable M/G/1 retrial queue: monotonicity and comparability

In this paper we investigate the monotonicity properties of an unreliable M/G/1 retrial queue using the general theory of stochastic ordering. We show the monotonicity of the transition operator of the embedded Markov chain relative to the strong stochastic ordering and increasing convex ordering. We obtain conditions of comparability of two transition operators and we obtain comparability conditions of the number of customers in the system. Inequalities are derived for the mean characteristics of the busy period, number of customers served during a busy period, number of orbit busy periods and waiting times. Inequalities are also obtained for some probabilities of the steady-state distribution of the server state. An illustrative numerical example is presented.     

Monotonicity in multidimensional Markov decision processes for the batch dispatch problem

Structural properties of stochastic dynamic programs are essential to understanding the nature of the solutions and in deriving appropriate approximation techniques. We concentrate on a class of multidimensional Markov decision processes and derive sufficient conditions for the monotonicity of the value functions. We illustrate our result in the case of the multiproduct batch dispatch (MBD) problem.     

Strong Law of Large Numbers and Central Limit Theorems for Functionals of Inhomogeneous Semi-Markov Processes

Limit theorems for functionals of classical (homogeneous) Markov renewal and semi-Markov processes have been known for a long time, since the pioneering work of Pyke Schaufele (Limit theorems for Markov renewal processes, Ann. Math. Statist., 35(4):1746–1764, 1964). Since then, these processes, as well as their time-inhomogeneous generalizations, have found many applications, for example, in finance and insurance. Unfortunately, no limit theorems have been obtained for functionals of inhomogeneous Markov renewal and semi-Markov processes as of today, to the best of the authors’ knowledge. In this article, we provide strong law of large numbers and central limit theorem results for such processes. In particular, we make an important connection of our results with the theory of ergodicity of inhomogeneous Markov chains. Finally, we provide an application to risk processes used in insurance by considering a inhomogeneous semi-Markov version of the well-known continuous-time Markov chain model, widely used in the literature.