该文研究了基于有限个数据点的随机Hough变换的概率模型。在这个模型中，主要讨论了在随机Hough变换的基本算法中起相当关键作用的两个量：累加器数组的控制阈值以及从图像中提取全部基元所需随机抽样的总次数这两个量对随机Hough变换的算法设计及其终止规则是相当有用的。该文的主要结果包括两部分：其一是对累加器数组引入了多项分布，系统地研究了累加器数组的概率结构及其相互关系。同时也计算了提取全部基元所需的随机抽样总次数的分布、均值和方差。另者是基于不断的随机抽样而使得累加器数组的随机变化作者引入了多维纯生过程，证明了提取全部基元所需随机抽样的总次数服从离散的PH分布，从而它的各阶矩都可用简洁的矩阵形式统一地表出。针对于图像的固有因素，作者也讨论了基元的平稳提取概率。该文的结果为随机Hough变换的进一步研究和应用提供了较为严格的理论依据。

系统地研究了两个不同并行服务台的可修排队系统MAP/PH（M/PH）/2，其中两个不同的服务台拥有一个修理工，若其中一台处于修理状态，则另一台失效后就处于待修状态，利用拟生灭过程理论，我们首先讨论了两个服务台的广义服务时间的相依性，然后给出了系统的稳态可用度和稳态故障度，最后得到了系统首次失效前的时间分布及其均值。

该文从概率的角度提出了两类新的滤波器：对称位相型滤波器和对称梯阶滤波器；证明了对任意给定的非负对称滤波器可用这两类滤波器的序列在（-∞，+∞）内一致逼近；这种序列有着统一的结构形式：对于L（x），文中给出了选择L（x）一些最优准则的解析表达式从而表明L（x）既具有一般性，又易进行解析处理和数值计算，对于已有文献中相关于对称指数滤波器的两类不同形式，例如Li等[6]和Ma等[9]，该文从理论上进一步刻画了它们的内在一致性。

In this paper, we study transition matrices of GI/M/1 type by using the approach proposed in Li and Zhao.[13] We obtain conditions on the a-classification of states for the transition matrix of GI/M/1 type. Unlike for matrices of M/G/1 type where association of the matrix multiplication can be easily justified, for matrices of GI/M/type, we first construct formal expressions for the β-invariant measure based on a representation of factorization of the transition matrix, and then show that it is a β-invariant measure directly. We also prove some spectral properties for the matrix of GI/M/1 type, which are not only used in constructing a formal expression for the b-invariant measure, but also of their own interest. We point out that the spectral analysis required for studying matrices of GI/M/1 type is much more sophisticated than that for matrices of M/G/1 type. Finally, we discuss connections of expressions for the b-invariant measure provided in this paper and in the literature.

In this paper, we provide UL-type and LU-type RG-factorizations for an irreducible continuous-time level-dependent quasi-birth-and-death (QBD) process with either finitely-many levels or infinitely-many levels and then apply the RG-factorizations to solve a class of linear QBD-equations which is always crucial for analyzing a stochastic model described as a QBD process Based on the results obtained for the linear QBD-equations we analyze up-, down-and return-integral functinals We explicityly express the Laplace transforms of the conditional distributions of the three types of stochastic integral functionals and their conditional moments.