Markov骨架过程的构造

本文讨论了Markov骨架过程的构造问题,把Dovb构造Markov过程的方法推广到Markov骨架过程的构造.     

Markov耦合与Markov过程的遍历性

本文运用耦合方法,真接通过无穷小算子判别随机过程的遍历性,得到了便于应用的遍历性定理。     

基于Markov过程的一类销售管理模型

本从实际背景出发，利用随机Q矩阵的Markov过程考察n个顾客的购物规律，得到了顾客在l时刻有i件商品的情况下，在t-l时间内离开商店的概率，从而解决了一类销售问题。     

两参数Markov过程的状态空间变换

设X=(Xr₎是有转移函数(P¹,P²,P)的两参数*-Markov过程,其中X_r取值于状态空间(E_r,(?)),r∈T=[0,∞)².对每个r∈T,设f_r是(E_r,(?)_r)到状态空间(E＇_r,(?)＇_r)中的可测变换.令Y_r=f_r(X_r),r∈T.给出了使Y=(Y_r)仍是有转移函数的两参数＊-Markov过程的充分条件,此条件加在转移函数(p¹,p²,p)和f_r上.对于有转移函数的两参数＊-Markov过程族,也讨论了类似的问题.     

Markov 骨架过程的随机时变换

讨论了Markov骨架过程的随机时变换,给出了一类变换Markov骨架过程为Markov骨架过程的随机时变换.     

Markov骨架过程积分型泛函的分布和矩及其应用举例

侯振挺等^[1]引入了一类具有广泛应用前景的随机过程－Markov骨架过程,本文研究这类过程积分型泛函的分布和矩及其计算问题,作为应用,我们得到了Doob过程,生灰2过程积分型泛函的分布和矩的公式,尤其对于生灭过程,利用本文的方法也得到了[4]中定理1－3的结果。     

“成批”顾客到达排队系统的Markov骨架过程模型

本文主要在原有的G/G/1排队系统的模型中,引入“成批”到达的概念,引入一次到达人数的随机变量ξ,讨论忙期闲期有关的情况.并通过对模型的讨论解决了带有选择的排队过程的分布情况.     

不动点与Markov过程的稳定性

运用不动点方法与耦合技巧得到一般状态空间上Markov过程平稳分布存在唯一性和KRW概率距离下的稳定性判据.作为应用,讨论了扩散过程的稳定性.     

高分子反应的Markov过程分析

以非线性缩聚反应模型为背景，定义了高分子反应的可逆Ｍａｒｋｏｖ过程，通过分析过程的配分函数，给出反应体系凝胶化存在的条件和确定其临界反应程度的方法，并得到当反应程度小于、等于和大于其临界值时，相应的平均分子量的分布．     

具有平均费用的非平稳Markov决策过程

本文研究了在一般状态空间具有平均费用的非平稳Ｍａｒｋｏｖ决策过程，把在平稳情形用补充的折扣模型的最优方程来建立平均费用的最优方程的结果，推广到非平稳的情形．利用这个结果证明了最优策略的存在性．     

A new generalized Laguerre spectral approximation and its applications

A new family of generalized Laguerre polynomials is introduced. Various orthogonal projections are investigated. Some approximation results are established. As an example of their important applications, the mixed spherical harmonic-generalized Laguerre approximation is developed. A mixed spectral scheme is proposed for a three-dimensional model problem. Its convergence is proved. Numerical results demonstrate the high accuracy of this new spectral method.     

A new generalized linear exponential distribution and its applications

A new generalized linear exponential distribution （NCLED） is considered in this paper which can be deemed as a new and more flexible extension of linear exponential distribution. Some statistical properties for the NGLED such as the hazard rate function, moments, quantiles are given. The maximum likelihood estimations （MLE） of unknown parameters are also discussed. A simulation study and two real data analyzes are carried out to illustrate that the new distribution is more flexible and effective than other popular distributions in modeling lifetime data.     

水库储水建模的马尔可夫骨架过程方法

在本中，我们应用马尔可夫骨架过程的理论，建立了水库储水模型，并且用向后方程刻画了水库储水过程的一维分布,这一模型是随机环境流体模型的推广，在金融管理以及网络技术等领域中都有重要应用．     

A class of path-valued Markov processes and its applications to superprocesses

Summary Let ( _s ) be a continuous Markov process satisfying certain regularity assumptions. We introduce a path-valued strong Markov process associated with ( _s ), which is closely related to the so-called superprocess with spatial motion ( _s ). In particular, a subsetH of the state space of ( _s ) intersects the range of the superprocess if and only if the set of paths that hitH is not polar for the path-valued process. The latter property can be investigated using the tools of the potential theory of symmetric Markov processes: A set is not polar if and only if it supports a measure of finite energy. The same approach can be applied to study sets that are polar for the graph of the superprocess. In the special case when ( _s ) is a diffusion process, we recover certain results recently obtained by Dynkin.     

A generalized duality and applications

The aim of this paper is to present a nonconvex duality with a zero gap and its connection with convex duality. Since a convex program can be regarded as a particular case of convex maximization over a convex set, a nonconvex duality can be regarded as a generalization of convex duality. The generalized duality can be obtained on the basis of convex duality and minimax theorems. The duality with a zero gap can be extended to a more general nonconvex problems such as a quasiconvex maximization over a general nonconvex set or a general minimization over the complement of a convex set. Several applications are given.On leave from the Institute of Mathematics, Hanoi, Vietnam.     

On determinantal representation for the generalized inverse A and its applications

In this paper, first we establish a determinantal representation for the group inverse A_g of a square matrix A. Based on this, a determinantal representation for the generalized inverse A is presented. As an application, we give a determinantal formula for the unique solution of the general restricted linear system: Ax=b(x ∈ T, b ∈ AT and dim(AT)=dim(T)), which reduces to the common Cramer rule if A is non‐singular. These results extend our earlier work. Copyright © 2006 John Wiley & Sons, Ltd.     

An improved generalized F-expansion method and its applications

An improved generalized F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the generalized nonlinear Schrodinger equation with a source to illustrate the validity and advantages of the proposed method. Many new and more general non-travelling wave solutions are obtained, including single and combined non-degenerate Jacobi elliptic function solutions, solitons-like solutions, trigonometric function solutions and rational solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in physics.     

QUATERNION GENERALIZED SINGULAR VALUE DECOMPOSITION AND ITS APPLICATIONS

This paper derives a theorem of generalized singular value decomposition of quaternion matrices （QGSVD）,studies the solution of general quaternion matrix equation AXB -CYD= E,and obtains quaternionic Roth＇s theorem. This paper also suggests sufficient and necessary conditions for the existence and uniqueness of solutions and explicit forms of the solutions of the equation.