广义生灭最小Q过程的可配称性

研究全稳定广义生灭最小Q过程的可配称性,获得广义生灭最小Q过程是可配称的充分必要条件,以及最小Q过程是唯一的可配称Q过程的充分必要条件．     

广义生-灭最小Q过程的常返、遍历性

研究具有突变率的全稳定广义生-灭最小Q过程的常返性和遍历性,在Q-矩阵是正则、不可约的条件下,利用Q过程的构造理论,获得广义生-灭最小Q过程是常返、遍历的易于检验的充分必要条件,并给出不变测度.     

The Stationary Distribution of a Continuous-Time Random Graph Process

ＴｈｅＳｔａｔｉｏｎａｒｙＤｉｓｔｒｉｂｕｔｉｏｎｏｆａＣｏｎｔｉｎｕｏｕｓ－ＴｉｍｅＲａｎｄｏｍＧｒａｐｈＰｒｏｃｅｓｓ韩东ＴｈｅＳｔａｔｉｏｎａｒｙＤｉｓｔｒｉｂｕｔｉｏｎｏｆａＣｏｎｔｉｎｕｏｕｓ－ＴｉｍｅＲａｎｄｏｍＧｒａｐｈＰｒｏｃｅｓｓ￥...     

Continuous-Time Markov Decision Processes with Unbounded Transition and Discounted-Reward Rates

Abstract

In this article, we study continuous-time Markov decision processes in Polish spaces. The optimality criterion to be maximized is the expected discounted criterion. The transition rates may be unbounded, and the reward rates may have neither upper nor lower bounds. We provide conditions on the controlled system's primitive data under which we prove that the transition functions of possibly non-homogeneous continuous-time Markov processes are regular by using Feller's construction approach to such transition functions. Then, under continuity and compactness conditions we prove the existence of optimal stationary policies by using the technique of extended infinitesimal operators associated with the transition functions of possibly non-homogeneous continuous-time Markov processes, and also provide a recursive way to compute (or at least to approximate) the optimal reward values. The conditions provided in this paper are different from those used in the previous literature, and they are illustrated with an example.     

带马尔可夫切换的Q过程的遍历性

本文应用Foster-Lyapunov不等式和耦合方法,研究了一类带马尔可夫切换的Q过程的指数遍历性和强遍历性; 同时,也构造了一些关于这类带马尔可夫切换的Q过程的耦合,并证明某些耦合是成功的.     

含瞬时态、具有突变率的广义生-灭Q-矩阵(I)

研究含瞬时态、具有突变率的广义生-灭拟q-矩阵,给出易于验证的Q过程存在性准则,并构造出全部Q过程和全部诚实Q过程,证明了不需附加任何条件,所有诚实Q过程都是常返的,给出诚实Q过程是遍历的充要条件,并求出其遍历测度,以及证明了不存在可配称Q过程.最后给出两个例子以说明我们的结果易于验证.     

含瞬时态、具有突变率的广义生-灭Q-矩阵(Ⅱ)

研究含瞬时态、具有突变率的广义生-灭拟q-矩阵,在Q_(E_0)非零流出下,给出易于验证的Q过程存在性准则,并构造出全部Q过程和全部诚实Q过程,证明了不需附加任何条件,所有诚实Q过程都是遍历的,并求出其遍历测度以及给出诚实Q过程可配称的充要条件。最后给出两个例子以说明本文的结果易于验证。     

基于Q-过程和随机模拟的病床安排方案

本文设计的一个新的住院病床安排方案,可用来取代传统的FCFS(先到先得)规则.患者在等候队列中的优先级将基于病情和手术的紧急程度.本文把患者的入住情况转化为经典的M/M/N排队论问题,利用可逆Q-过程的性质以及经典排队论的结果,得到各类疾病患者的平均逗留时间以及所需床位数的先验估计.根据独立Poisson过程的性质确定排队过程的Q-矩阵,从而作出相应的先验估计和具体表达式.在若干约束条件的基础上,利用C++编程求得最优病床分配方案.本文建立的评价指标体系,通过计算机随机模拟,证明了在多种情形下,该模型较FCFS(先到先得)规则更具优势.     

广义生-灭最小Q过程及其性质

本文给出具有突变率的广义生－灭最小Q过程及其性质。     

Critical age-dependent branching process diffusions

Two diffusions are derived as the limits in finite dimensional distributions of appropriately conditioned and scaled critical age-dependent branching processes. A technical lemma about the asymptotic behavior of the joint generating function is used to overcome the difficulties introduced by the non-Markov nature of the process. The results are extensions of those of Lamperti and Ney [5] for Galton-Watson processes. Also, the “age-dependent Q-process” is defined and its transition probabilities obtained.