记录时间的联合分布

使用组合数学与概率论的方法研究了记录时间示性符之和的分布,并得出两个不相邻的记录时间L(n)和L(m)的联合分布.     

k阶记录时间的联合分布

使用组合数学与概率论的方法研究了k阶记录时间示性符之和的分布,并得出两个不相邻的k阶记录时间L(n,k)和L(m,k)的联合分布.     

记录值的联合分布

使用组合数学与概率论的方法研究了记录值示性符之和的分布,并得出第i个记录值X(i)的概率分布及记录值X(j)和X(i)的联合分布.     

关于k阶记录时间与k阶记录值的联合分布

设独立同分布随机变量序列{x_nj n≥1}的分布函数F(x)=p(x₁(k)(n);n≥1},{X^(k)(n);n≥1} 分别为{x_nj n≥1}的K阶记录时间序列和k阶记录值序列.本文我们用直接方法求出了{U^(k)(i),X^(k)(i);1≤i≤n}的联合分布，从而证明了k阶记录时间序列及k阶记录值序列的马氏性，并导出了它们之间的一     

一种均匀分布的修正分布——UR-n分布

从现实应用中 ,提出一种均匀分布的修正分布 ,并进一步研究了n次修正分布———UR n分布的性质及其极限性质 .这一分布在军事中武器精度的研究、天文观测等多方面都很有利用价值 .     

一类特殊分布纪录值之和的中心极限定理

摘要：设{X，Xn,n≥1)为独立同分布的服从某连续分布F的随机变量序列，X^(1)=X1，X^(2),X^(3),…为其纪录值序列．令ψ(u)=F^-1(1-e^-u)．其中F^-1是F的反函数．本文研究当ψ(u)=log^pu时Tn=∑k=1^nX^(k)=^dn∑k=1^nψ(Sn)的极限性质．解决了户为所有正整数时Tn的中心极限定理．     

一类特殊Weibull分布纪录值之和的中心极限定理

给出了参数τ为正整数的倒数为Weibull分布纪录值之和的中心极限定理。     

对数正态型分布纪录值之和的渐近分布

设X₁ , X₂, …是i.i.d.的随机变量序列, X⁽¹⁾ ,X⁽²⁾, …是它的纪录值序列. 对X₁∈LN( γ ), 即X₁服从对数正态型分布的场合, 讨论纪录值的部分和序列 的渐近分布问题. 发现γ = 2是一个分界线, 并且证明了在γ ＞2时, T_n渐近于正态分布; 而在2＞γ＞1时, T_n在通常的中心化和正则化之下, 不能收敛到任何非退化的概率分布, 但是此时log T_n渐近于正态分布.     

离散PH分布的一个封闭性质及其应用

本证明了离散PH分布的一个封闭性质并讨论了它在离散时间排队研究中的应用。     

相切于定三角形三边的二阶曲线的伴随点及其分布

证明了相切于定三角形三边的二阶曲线与三角形三边所在直线外的点(伴随点)一一对应,并得出各类型伴随点的分布情况.     

Invariance Principles for Paced Record Times and Applications

Let {Y_n:n0} be a sequence of independent and identically distributed random variables with continuous distribution function, and let {N(t):t0} be a point process. In this paper, making use of strong invariance principles, we establish limit laws for the paced record process {X(t):t0} based on {Y_n:n0} and {N(t):t0}. We consider as applications of our main results, the case of the classical and paced record models. We conclude by extensions of our theorems to non-homogeneous record processes.     

On the Number of Records in an iid Discrete Sequence

The problem of the rate of growth of the number of record values and weak record values in an iid sequence of integer valued random variables is attacked as a perturbation of the case for continuous random variables. Conditions in terms of either the underlying probability mass function or the hazard function of the underlying distribution are given for the rate of growth of the number of records to be log(n) almost surely. The record problem has been considered by Gouet et al.(2001) [Adv. Appl. Prob. 33, 473-864] and by Vervaat(1973) [Stochastic processes Appl. 1, 317-334]. The results for records overlap those found in the former paper. The methods here are more elementary, and the results on weak records are not mentioned there. This paper improves on what may be derived from results in Vervaat. (1973) [Stochastic Processes Appl. 1, 317-334] An erratum to this article can be found at     

非线性加工时间单机排序问题

讨论工件加工时间是等待时间的非线性增加函数的单机排序问题,目标函数为极小化完工时间和与极小化最大延误.基于对问题的分析,对于一般非线性函数的情况,给出了工件间的优势关系.对于某些特殊情况,利用工件间的优势关系得到了求解最优排序的多项式算法.推广了文献中的结论.     

Brown运动的逗留时与首中时

设为中的标准Brown运动,对0＜α,记本文求出了X在首中球面之前逗留在Bα内的时间的Laplace变换,在首中之前逗留在Bαb内的时间的Laplace变换以及在首中之前逗留在Bαb内的时间的Laplace变换．作为推论,求出了X关于球面首中时的Laplace变换,逗留在球内总的时间的Laplace变换及逗留在球壳内的总的时间的LaPlace变换．     

Delay Distribution of (Im)Patient Customers in a Discrete Time D-MAP/PH/1 Queue with Age-Dependent Service Times

This paper presents an algorithmic procedure to calculate the delay distribution of (im)patient customers in a discrete time D-MAP/PH/1 queue, where the service time distribution of a customer depends on his waiting time. We consider three different situations: impatient customers in the waiting room, impatient customers in the system, that is, if a customer has been in the waiting room, respectively, in the system for a time units it leaves the waiting room, respectively, the system. In the third situation, all customers are patient – that is, they only leave the system after completing service. In all three situations the service time of a customer depends upon the time he has spent in the waiting room. As opposed to the general approach in many queueing systems, we calculate the delay distribution, using matrix analytic methods, without obtaining the steady state probabilities of the queue length. The trick used in this paper, which was also applied by Van Houdt and Blondia [J. Appl. Probab., Vol. 39, No. 1 (2002) pp. 213–222], is to keep track of the age of the customer in service, while remembering the D-MAP state immediately after the customer in service arrived. Possible extentions of this method to more general queues and numerical examples that demonstrate the strength of the algorithm are also included.     

Almost sure limit points of and the number of boundary crossings related to SLLN and LIL for record times,inter-record times and the number of record values

In this paper, the almost sure limit points and the moments of the number of boundary crossings of some functions of record times, inter-record times and the frequency of record values of a sequence of independent and identically distributed continuous random variables are studied.