关于l~p－值Gauss过程增量的若干结果

本文讨论了具有平稳增量的ｌｐ－值Ｇａｕｓｓ过程　的Ｃ、－Ｒ增量的若干下极限结果，也讨论了一类滞后增量有多大及其相应下极限结果，把关于Ｗｉｅｎｅｒ过程成立的结果，在一定条件下拓广到ｌｐ－值Ｇａｕｓｓ过程上．     

关于Gauss过程若干强极限定理

本文讨论了具有平稳增量的Ｇａｕｓｓ过程，在（０≤ｒ≤∞）时这类Ｇａｕｓｓ过程的增量有多小的问题．把有关的Ｗｉｅｎｅｒ过程的结果，在一定的条件下，推广到这类Ｇａｕｓｓ过程上去．此外还讨论了另一种形式的不可微模．     

M／M／1／k后馈系统中的随机过程

本文对Ｍ／Ｍ／１／ｋ后馈排队系统中各随机过程的Ｐｏｉｓｓｏｎ性进行了讨论，推广了Ｂｒｅｍａｕｄ（［２］，［３］）的相应结果。所得结论表明Ｍ／Ｍ／１／ｋ后馈系统与Ｍ／Ｍ／１后馈系统情况有所不同，即在某些情况下，除总输出过程外，还有其它的过程也可能是Ｐｏｉｓｓｏｎ过程。顺便又地Ｍ／Ｍ／Ｃ／ｋ前馈后馈排队系统的动态数学模型进行了严格的讨论。     

l~∞－值Gauss过程的增量有多大

本文在一定条件下给出了ｌ∞－值Ｇａｕｓｓ过程增量有多大，并把它应用于一类ｌ∞－值Ｏｒｎｓｔｅｉｎ－Ｕｈｌｅｎｂｅｃｋ过程上，给出相应结论．     

L^2-策略休假下可修的M_1+M_2/G^x(M/G)/1匹配排队系统分析

双输人匹配排队系统是通常排队系统的一种推广．本文对该系统考察了Ｌ２－策略休假和服务台可修的两个重要因素．其中假定系统有两个不同的Ｐｏｉｓｓｏｎ输入，两类顾客按１：１作成一批进行服务，服务台的寿命服从指数分布，服务时间，修理时间和休假时间都服从一般连续型分布，利用向量马氏过程方法，得到了该排队系统的一些重要的稳态排队论指标和可靠性指标．     

带迁入的分枝粒子系统的波动极限

本文研究了一个带迁入的对称稳定粒子系统，对此系统作时间和空间的重新标度，得到了重新标度过程的一个大数定律，证明了重新标度过程的波动极限是Ｏｒｎｓｔｅｉｎ－Ｕｈｌｅｎｂｅｃｋ超过程．     

有限维Brusseltor模型的正常返性

本文证明了多物种反应扩散过程的一种基本模型－Ｂｒｕｓｓｅｌｔｏｒ模型在有限维情形下总是正常返的，因而是遍历的，事实上还是指数遍历的。     

随机分形

本文概括了随机分形的主要结果，综述了随机分形的最新进展和目前的动态，提出了一些末解决的问题，全文共分为三部分：（１）由随机过程和随机场（如Ｌｅｖｙ过程，Ｇａｕｓｓ场，自相似过程等）产生的各种随机分形集（如象集、水平集、Ｋ重点集等）的Ｈａｕｓｄｏｒｆｆ维数、测度和ｐａｃｋｉｎｇ维数、测试；（２）随机Ｃａｎｔｏｒ型集和统计自相似集的维数和测试；（３）分形集（如Ｓｐｉｅｒｐｉｎｓｋｉ ｇａｓｋｅｔ，ｎｅ     

具有多个奇点的广义的Lienard系统不存在任何闭轨的条件

本文不同于一般的方法，利用辅助函数建立了具有多个奇点的广义的Ｌｉｅｎａｒｄ系统不存在任何闭轨的若干判别条件。关于的经典的Ｂｅｎｄｉｘｓｏｎ判别法则和Ｐｏｉｎｃａｒｅ地形系法则是其特例。此外，给出了包括三次振动系统系统在内的例子。     

关于Φ-伪压缩型映象的具误差的Ishikawa和Mann迭代过程的收敛性问题

往Ｂａｎａｃｈ空间中．研究了多值Φ－伪压缩型映象的具误差的Ｉｓｈｉｋａｗａ和Ｍａｎｎ迭代过程的收敛 性问题，所得结果改进、发展和统一了许多人的最新结果．     

A queue with a pair of instantaneous independent bernoulli feedback processes

In this paper we are concerned with several random processes that occur in M/G₂/l queue with instantaneous feedback in which the feedback decision process is a pair of independent Bernoulli processes. The stationary distribution of the output process has been obtained. Results for particular queues with feedback and without feedback are obtained. Some operating characteristics are derived for this queue. Some interesting results are obtained for departure processes. Optimum service rate is obtained. Numerical examples are provided to test the feasibility of the queueing model     

Analysis of the discrete-time bulk-service queue Geo/G/1/N+B

This paper considers a discrete-time bulk-service queueing system with variable capacity, finite waiting space and independent Bernoulli arrival process: Geo/G^Y/1/N+B. Both the analytic and computational aspects of the distributions of the number of customers in the queue at post-departure, random and pre-arrival epochs are discussed.     

GI／PH／1休假排队系统队长的随机分解

对空竭服务、多重休假规则的GI/PH/1排队系统的稳态行为给出了详尽分析。在休假时间服从负指数分布情况下,讨论了到达点嵌入Markov链的结构、平衡条件和稳态队长。证明稳态队长可分解成两个独立随机变量之和。     

Asymptotic Independence and Additive Functionals

A strong approximation result is proved for the partial sum process of i.i.d. sequence of vectors having dependent components, where the components of the approximating process are independent. This result is applied for additive functionals of random walks in one and two dimensions.     

Multi-server retrial queue with negative customers and disasters

We consider a multi-server retrial queue with waiting places in service area and four types of arrivals, positive customers, disasters and two types of negative customers, one for deleting customers in orbit and the other for deleting customers in service area. The four types of arrivals occur according to a Markovian arrival process with marked transitions (MMAP) which may induce the dependence among the arrival processes of the four types. We derive a necessary and sufficient condition for the system to be positive recurrent by comparing sample paths of auxiliary systems whose stability conditions can be obtained. We use a generalized truncated system that is obtained by modifying the retrial rates for an approximation of stationary queue length distribution and show the convergence of approximation to the original model. An algorithmic solution for the stationary queue length distribution and some numerical results are presented.      

Pathwise convergence rates for numerical solutions of Markovian switching stochastic differential equations

This work develops numerical approximation algorithms for solutions of stochastic differential equations with Markovian switching. The existing numerical algorithms all use a discrete-time Markov chain for the approximation of the continuous-time Markov chain. In contrast, we generate the continuous-time Markov chain directly, and then use its skeleton process in the approximation algorithm. Focusing on weak approximation, we take a re-embedding approach, and define the approximation and the solution to the switching stochastic differential equation on the same space. In our approximation, we use a sequence of independent and identically distributed (i.i.d.) random variables in lieu of the common practice of using Brownian increments. By virtue of the strong invariance principle, we ascertain rates of convergence in the pathwise sense for the weak approximation scheme.     

独立增量过程的一个强逼近定理

该文给出了独立增量过程的一种强逼近定理,由此得到相应的ｓｔｒａｓｓｅｎ重对数律．     

On the Local Time of the Weighted Bootstrap and Compound Empirical Processes

This article is mainly concerned with the local times of the weighted bootstrap process. We prove a strong approximation theorem for the local time of the weighted bootstrap process by the local time of a Brownian bridge. We consider also the local time of the compound empirical processes that can be seen, asymptotically, as the local time of the convolution of two independent Gaussian processes.     

Empirical distributions in marked point processes

We study the asymptotic behaviour of the empirical distribution function derived from a stationary marked point process when a convex sampling window is expanding without bounds in all directions. We consider a random field model which assumes that the marks and the points are independent and admits dependencies between the marks. The main result is the weak convergence of the empirical process under strong mixing conditions on both independent components of the model. Applying an approximation principle weak convergence can be also shown for appropriately weighted empirical process defined from a stationary d-dimensional germ-grain process with dependent grains.     

A new renewal approximation for certain autocorrelated processes

We propose a new renewal approximation for autocorrelated streams with limiting index of dispersion less than unity. The superposition of independent processes and the splitting of an autocorrelated process are studied. The proposed approximation performs well on predicting the mean delay in a single server queueing system receiving autocorrelated processes.