布朗运动的若干结果

1827年,英国生物学家布朗(R.Brown)观察到微小的粒子在液体(或气体)中不停地作极不规则的运动,这一发现在科学界产生了很大的影响。时间已经过去165年,关于这种运动的数学研究论文仍然层出不穷。国际上著名的几种概率论杂志中,几乎每期都有关于布朗运动的论文。1 一维布朗运动从发现到理论的建立经历了漫长的时间,其中有许多卓越人物的工作。1905年,爱因斯坦认为运动是由于微粒受到液体中大量分子的碰撞(每秒10~(20)次)而引起的。微粒在t时的位置x_t是随机的。假设x_0=0,以p(t,x)表x_t的一个坐标分量的分布密度,在一定条件下,他得到。     

全稳定Q过程构造的一个等价条件

给出了Q过程构造的等价条件,证明了Q过程的构造等价于一个条件方程组的解,以此方法求出了所有的Q过程、F过程、B过程及BF过程的等价条件。     

一类向量高斯过程之上穿过点过程的渐近分布

｛Ｘ（ｔ），ｔ≥｝为ｐ维高斯过程，在一定条件下，本文得到了｛Ｘ（ｔ），０≤ｔ≤Ｔ｝对水平ＵＴ（＞０）的ε－上穿过次数所形成的点过程的渐近分布（Ｔ→∞）。证明了Ｐ个分量点过程的渐近独立性。     

一类两指标过程—EARMA过程

本文将两指标 ARMA 过程加以推广,提出了一类新的两指标弱平稳过程——EARMA 过程,给出了它的平稳性条件和可逆性条件;讨论了它的若干性质;并讨论了它的参数估计,其中主要是自相关估计的强相合速度。     

两指标Levy过程的强极限定理

本文研究了两指标Ｌｅｖ过程增量平方和的强极限，获得了一些重要结果。     

广义n参数Wiener过程和广义OUPn的导出过程的注记

记为非负单增函数且一阶偏导数均存．本文证明：（ｉ）广义ｎ参数Ｗｉｅｎｅｒ过程（ＧＢｎ）和广义ｎ参数Ｏｒｎｓｔｅｉｎ－Ｕｈｌｅｎｂｅｃｋ过程（广义ＯＵＰｎ）在Ｄ中导出的过程是马氏过程；（ｉｉ）如果ＧＢｎ（或广义ＯＵＰｎ）在Ｄ中导出的过程成为某个ＧＢｋ（或某个广义ＯＵＰｋ），则ｆｊ（ｔ１…，ｔｋ）未必恒为正常数．（ｊ＝ｋ＋１，…，ｎ）．     

扩散过程的极性的一个充分条件

本文研究非退化多维扩散过程的极性，得到了一个充分条件。     

有关对偶方程的充要条件

本文给出了多维马氏过程的对偶过程存在的充分必要条件,在多维跳过程的情形下,本文给出了用Q-对来验证对偶过程是否存在的条件。     

条件马尔可夫过程的表示

设函数空间型马氏过程 X=(Ω,(?),(?)_t,X_t θ_t,P~x)是以(E,(?))为状态空间的暂留的Hunt 过程,ξ为(E,(?))上 Radon 测度,X 的位势核 U(x,A)=integral A u(x,y)ξ(dy),而 u(x,y)满足 chung、Rao[6]的基本假定。我们找到了一个由 u(x,y)确定的零势集∧(等价于ξ(∧)=0),证明了下述结论:定理 设μ为(?)上测度,μ(∧)=0,h=Uμ(?)∫u(·y)ξ(dy).记 E~h={0相似文献   

扩散过程代数式收敛定性的判别准则

本文定性地讨论非紧空间中可逆扩散过程的代数式收敛的判定 .使用分裂空间的方法 .将全空间分裂成两个部分 :紧的子空间与非紧的余子空间 .在紧子空间中考虑边界反射的Neumann过程 ,它必然是代数式收敛的 .而在非紧子空间中考虑边界吸收的Dirichlet过程 ,如果这一Dirichlet过程以代数式的速度击中边界 ,那么就有原过程在全空间代数式收敛 ;反之 ,原过程代数式收敛 ,非紧子空间中的Dirichlet过程也是代数式收敛的 .因此过程在紧子空间的任意摄动不会影响在全空间的代数式收敛性 .     

Finding upper-triangular representations for phase-type distributions with 3 distinct real poles

In this paper we seek particular representations for absolutely continuous Phase-type distributions with 3 distinct real poles. First, we define subsets of these Phase-type distributions given the 3 distinct poles. One subset contains distributions that have upper triangular PH representation of order n, but do not have a triangular one of PH order n−1. This is done by using the invariant polytope approach. For any distribution in our subsets we give an invariant polytope containing the corresponding distribution by finding the vertices of the polytope. Second, we propose a method that actually constructs the generator matrix of the required PH representation from the invariant polytope. Consequently, our method constructs an upper triangular PH representation that has minimal order among the upper triangular PH representations given the probability density function of a PH distribution.     

一个机器服务模型的可靠性分析

本文讨论了由Ｎ个同型部件和一个服务设备组成的机器服务模型，在服务设备绝对可靠，或服务设备具有指数寿命，修理工对其修理的时间为ＰＨ分布，这两种情况下求得了系统的平稳概率分布，从而求得机器系统和服务设备的稳态可靠性指标，并证明了它们的首次失效时间均服从ＰＨ分布，服务设备和修理工的忙期亦服从ＰＨ分布．     

Why certain discrete phase type representations have numerically stable spectral decomposition

The discrete-time phase type (PH) distributions are used in the numerical solution of many problems. The representation of a PH distribution consists of a vector and a substochastic matrix. The common feature of the PH distributions is that they have rational moment generating function. The moment generating function depends on the eigendecomposition of the transition probability matrix of the PH distribution, but the eigenvalues and eigenvectors are important in other cases as well. Due to the finite precision of the numerical calculations or other reasons, a representation may contain errors that change the eigendecomposition. This paper presents upper bounds on the change of the eigendecomposition when the PH representation is perturbed. Since these bounds do not depend on a particular representation, but they hold for all, the analysed PH representations have uniformly stable spectral decompositions.      

极值分布的一个注记

本文对PH极值分布进行了推广,应用构造相关联的Markov过程的方法,证明了n个相互独立的PH随机变量构成的次序随机变量的分布仍是PH分布。并给出了次序PH随机变量分布表达式的表示方法,本文同时也给出了次序PH随机变量的联合生存分布,本文最后给出了次序PH随机变量在可靠性理论与更新理论中的应用。     

Sojourn time distributions in the queue defined by a general QBD process

We consider a general QBD process as defining a FIFO queue and obtain the stationary distribution of the sojourn time of a customer in that queue as a matrix exponential distribution, which is identical to a phase-type distribution under a certain condition. Since QBD processes include many queueing models where the arrival and service process are dependent, these results form a substantial generalization of analogous results reported in the literature for queues such as the PH/PH/c queue. We also discuss asymptotic properties of the sojourn time distribution through its matrix exponential form.     

����Ŀ��ʱ�����ɢPH�ֲ����ʾ

本文研究毁伤目标离散时间的概率分布和PH表示.在射击时间间隔服从离散PH分布的条件下,本文导出了不考虑发现目标因素和考虑该因素二种情况下,毁伤目标时间的离散PH表示与分布.同时,文章用实例说明了求毁伤目标离散时间的PH表示、概率分布和毁伤目标平均离散时间的方法.     

The matched queueing network PH/M/c→oPH/PH/1

We consider a matched queueing network PH/M/coPH/PH/1, where the output of the first subsystem PH/M/c is regarded as one of the inputs of the second subsystem and matched with another input of PH-renewal process, and they are served by a single server with PH-service-distribution. The stationary state probabilities, the distribution of the virtual waiting times in the two subsystems, and the distribution of the total virtual waiting time are derived.The work was supported by the Max-Planck-Gesellschaft, Germany, and the Chinese Academy ofSciences.     

Fitting correlated arrival and service times and related queueing performance

In this paper, we consider a queue where the inter-arrival times are correlated and, additionally, service times are also correlated with inter-arrival times. We show that the resulting model can be interpreted as an MMAP[K]/PH[K]/1 queue for which matrix geometric solution algorithms are available. The major result of this paper is the presentation of approaches to fit the parameters of the model, namely the MMAP, the PH distribution and the parameters introducing correlation between inter-arrival and service times, according to some trace of inter-arrival and corresponding service times. Two different algorithms are presented. The first algorithm is based on available methods to compute a MAP from the inter-arrival times and a PH distribution from the service times. Afterward, the correlation between inter-arrival and service times is integrated by solving a quadratic programming problem over some joint moments. The second algorithm is of the expectation maximization type and computes all parameters of the MAP and the PH distribution in an iterative way. It is shown that both algorithms yield sufficiently accurate results with an acceptable effort.     

具有位相型随机补货提前期的PH退化可修系统及其最优更换策略

将几何过程与PH分布相结合, 讨论一个带有位相型随机补货提前期的PH退化可修系统.通过建立最小生成元$Q$矩阵,获得了系统在稳态情形下的状态概率分布向量及其数值解.根据上述研究结果同时也得到了系统的几个重要可靠性指标. 进一步地,还考虑了基于部件故障次数的订购策略和更换策略,导出系统单位时间平均运行成本的解析表达式并给出一个确定最优$N$策略的数值算例.     

基于几何过程和位相分布休假的两部件并联可修系统的可靠性分析

主要以两不同型部件组成的并联可修系统为研究对象.在系统对失效相位存在记忆的基础上,考虑了修理工可单重休假且休假时间服从位相(PH)分布.每个工作部件均有可能因受到两种不同类型的故障而失效,且均"修复非新".在假定部件的工作时间,修理时间分别服从PH分布的几何过程和负指数分布的条件下,利用马尔可夫过程和矩阵分析的方法,对可修系统进行了可靠性分析,并给出了相应可靠性指标的数值算例.