理赔为一般到达的常利率风险模型

本文研究了一般到达的常利率保险风险问题，应用建立Markov骨架过程的方法建立了理赔为一般到达的常利率风险模型．给出了破产时的余额分布、破产前瞬间的余额分布、破产时间与破产前瞬间余额的联合分布、破产时间与破产时余额的联合分布及破产前瞬间余额、破产时余额与破产时间的联合分布．     

一类拟平稳序列极值的极限律

Ｋ．Ｆ．Ｔｕｒｋｍａｎ讨论了一类拟平稳序列最大值的渐近分布。本文利用点过程收全党一理得到水平超出点过程的收敛定理和第ｒ个最大值的渐近分布及前ｒ个最大值的联合渐近分布。     

一类Gauss序列极值的极限律

本文讨论一类非平稳Gauss序列的极值．利用点过程收敛定理得到多水平超过的点过程的收敛性,同时得到在不相交区间上最大值的联合渐近分布,第k个最大值的渐近分布以及前r个极值的联合渐近状态．     

非负整值随机变量序列的一类强偏差定理

设是在中取值的一列随机变量，其联合分布为是S上的一个分布，该文研究对数似然比与之间的若干极限关系，得到了一类用不等式表示的强极限定理（称之为强偏差定理），其偏差界依赖于样本点．证明中结合区间刻分法，提出了将母函数的工具应用于强极限定理研究的一种途径．     

随机区间[0,T]上混合泊松过程的相关性质

本文定义出一类新的计数模型随机时间区间[0,T]上的混合泊松过程{Nt,0≤t≤T}并验证了其不再具有平衡性和独立增量性,从而与常见的泊松过程不同.文中给出了n个质点发生时刻S1,…,Sn的条件联合分布和n个点间时间间隔T1,…,Tn的联合分布.在一定适当假设下,文中给出了一个其在排队论中应用较多的封闭性定理.     

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．     

供应链中的MQ(t)/Gj/∞排队群

本文研究由一个非时齐Poisson到达过程驱动的多个MQ(t)／Gj／∞型排队系统．当一个K型到达发生时(K(?){1,…,m}),对每一个j∈K,顾客按批量QjK进入排队系统j,(Q1K,…,QmK)是相依的随机向量．我们导出了联合队长过程和联合输出过程的多变量母函数,并给出各排队系统之间的相关性分析．这些结果为非时齐供应链分析提供了理论依据     

一类索赔相关且带干扰的风险模型

该文讨论了索赔时间间隔与索赔量相关且带干扰的风险模型. 借助拉普拉斯变换研究了此模型的破产时刻、破产前瞬间盈余及破产时赤字三者的联合分布,得到了此联合分布拉普拉斯变换的一个分析表达式并讨论了当初始盈余值趋于无穷大时,此联合分布的渐近表达式.     

如何发现世界上最安静的敌潜艇

我们建立了一个数学模型；用以探测一个大型移动目标，譬如说一艘潜艇．并且计算出潜艇的大小和它移动的速度、方向．探测过程仅依赖于一个普通噪声环境受到的扰动我们作了一系列合理的假设，分析了潜艇的运动以及它对背景噪声场的影响．运动潜艇吸收、反射噪声声波，由此产生的多普勒效应，是原噪声场的一个扰动．这种扰动可被探测器（如压电麦克风）捕获．在对潜艇的形状与材料作了假设的基础上，我们推导出在一个单频单幅噪声场中潜艇回波的频谱分布．这个频谱分布类似伞形，简称伞形分布．频谱带宽可用于计算潜艇航速．伞形分布曲线下的面积可用于计算潜艇等效截面积，根据频谱的中心频率与噪声频率的差异，可计算出它的移动方向我们引入了对数频率坐标．基于卷积理论，计算出了在宽带噪声场中潜艇的回波．这样，通过反卷积，就可以简化为上述己解决的若这艘潜艇置于一单频单幅噪声场中应有的情况．根据反卷积后的回波分布，即可根据本文中提到的方法，得到需要的结果．我们还把这个模型推广到实际中，给出了一个伺服系统和一个可行的方案．文中最后就模型优缺点和问题本身的局限性作了讨论．考虑到实际的应用，提出了一些新的构想，并预想了这类问题今后可能的发展方向．     

一种Tandem网络模型

本文考虑的是一个MAP输入的tandem队列，运用一个新颖的方法把它模拟成一个带爆炸块依赖阶数的拟生灭过程，这样使得我们可以很好地分析它的联合时间分布和平稳状态的停留时间分布布。     

CROSSING TIME AND RENEWAL NUMBERS OF TWO PH-RENEWAL PROCESSES

This paper considers how to find some joint distributions and their marginal distributions of crossing time and renewal numbers related to two PH-renewal processes by constructing an absorbing Markov proems.     

Distribution of order statistics of waiting times in an ordinary renewal process and the covariance of the renewal increments

The joint distribution of inter–renewal times and the number of renewals is used to derive joint and marginal distributions of order statistics of waiting times of an ordinary renewal process. Also, expressions are obtained for the covariance function of the number of renewals and of the renewal increments in an ordinary renewal counting process in terms of the renewal function     

Some Results for the Compound Poisson Process That Is Perturbed by Diffusion

Abstract In the present paper surplus process perturbed by diffusion are considered.The distributions ofthe surplus immediately before and at ruin corresponding to the probabilities of ruin caused by oscillation andruin caused by a claim are studied.Some joint distribution densities are obtained.Techniques from martingaletheory and renewal theory are used.     

保费到达为平衡更新过程的复合更新风险模型

本文研究保费到达为平衡更新过程的复合更新风险模型 ,给出了有限时间内的生存概率分布 ,破产时间 T与破产时资产盈余 U(T)的联合分布 ,及破产时间 T与破产前瞬时盈余 U(T- )的联合分布 .     

The expected discounted penalty function under a renewal risk model with stochastic income

In this paper, we consider a renewal risk model with stochastic premiums income. We assume that the premium number process and the claim number process are a Poisson process and a generalized Erlang (n) processes, respectively. When the individual stochastic premium sizes are exponentially distributed, the Laplace transform and a defective renewal equation for the Gerber-Shiu discounted penalty function are obtained. Furthermore, the discounted joint distribution of the surplus just before ruin and the deficit at ruin is given. When the claim size distributions belong to the rational family, the explicit expression of the Gerber-Shiu discounted penalty function is derived. Finally, a specific example is provided.     

Estimation in Stationary Markov Renewal Processes,with Application to Earthquake Forecasting in Turkey

Consider a process in which different events occur, with random inter-occurrence times. In Markov renewal processes as well as in semi-Markov processes, the sequence of events is a Markov chain and the waiting distributions depend only on the types of the last and the next event. Suppose that the state-space is finite and that the process started far in the past, achieving stationary. Weibull distributions are proposed for the waiting times and their parameters are estimated jointly with the transition probabilities through maximum likelihood, when one or several realizations of the process are observed over finite windows. The model is illustrated with data of earthquakes of three types of severity that occurred in Turkey during the 20th century.AMS 2000 Subject Classification: 60K20     

有优先权且有两不同修理设备的两部件冷贮备可修系统的可靠性分析

在开关不完全可靠的情况下,研究了两个不同型部件和两个修理设备组成的冷贮备系统.在部件1有工作和修理优先权的条件下,建立了在部件和开关工作寿命及修理时间均服从指数分布的可修系统模型,利用Markov理论和Laplace变换,给出了系统可靠度的Laplace表达式及系统的稳态指标.     

Bernoulli thinning of a Markov renewal process

A Bernoulli thinning of a Markov renewal process is investigated. The properties of the thinned process are considered and are related to the properties of the original process. The parameters, moments and equilibrium of the thinned process are determined in terms of the parameters defining the underlying Markov renewal process. Results are illustrated by examples. © 1998 John Wiley & Sons, Ltd.     

A modified insurance risk process with uncertainty

An insurance risk process is traditionally considered by describing the claim process via a renewal reward process and assuming the total premium to be proportional to the time with a constant ratio. It is usually modeled as a stochastic process such as the compound Poisson process, and historical data are collected and employed to estimate the corresponding parameters of probability distributions. However, there exists the case of lack of data such as for a new insurance product. An alternative way is to estimate the parameters based on experts’ subjective belief and information. Therefore, it is necessary to employ the uncertain process to model the insurance risk process. In this paper, we propose a modified insurance risk process in which both the claim process and the premium process are assumed to be renewal reward processes with uncertain factors. Then we give the inverse uncertainty distribution of the modified process at each time. On this basis, we derive the ruin index which has an explicit expression based on given uncertainty distributions.     

Counting the number of renewals during a random interval in a discrete-time delayed renewal process

In a discrete-time delayed renewal process, we study the distribution of the number of renewals during a random interval. We obtain closed-form expressions for the probability mass function and binomial moments of this number for various distributions of the random interval and interrenewal times.