一类分支过程的收敛性

随机稳定性是各种随机模型中的至关重要的问题,随机稳定性中的关键问题是找出过程遍历,指数遍历和强遍历的准则．该文对一类重要的分支过程给出了过程指数遍历及强遍历的条件．在证明中主要应用了几种不同的比较方法,从该文的结果可以看出,这种方法是有效的,因而在其它情形中也是非常有意义的．而且所得结果的概率意义也是十分清楚的．     

一类非齐次马氏链的绝对平均强遍历性

引用马氏链绝对平均强遍历的概念,首先给出齐次马氏链绝对平均强遍历与强遍历的等价性,其次通过引进另一个强遍历的非齐次马氏链,给出一个非齐次马氏链绝对平均强遍历的充分条件.     

拓扑遍历与拓扑双重遍历

令X为紧致度量空间,f:X→X为连续映射,U,V为X的任意非空开集,若{n>0|fn(U)∩V≠ )为正上密度集,则称f拓扑遍历.f拓扑双重遍历意味着f×f拓扑遍历.本文在[2]的基础上进一步讨论拓扑遍历与拓扑双重遍历映射的性质.     

有限域上遍历矩阵的特性研究

对有限域上遍历矩阵的性质进行了分析,给出了有限域上遍历矩阵的计数定理,并对遍历矩阵序对(A,B)关于矩阵M的双侧幂乘集〈A〉M〈B〉的秩及基数进行了全面分析.给出了R_k(A,B)集的构成及其基数的有关定理,所得到的结论对利用遍历矩阵实现有关的公钥密码具有理论上的指导意义.     

关于遍历测度乘积的遍历性

本文利用拟特征标序列收敛的零一律与遍历测度的关系,讨论了遍历测度乘积的遍历性．     

广义算子半群的遍历及概率逼近定理

首先给出了广义算子半群的Abel-遍历和Cesaro-遍历的定义,对两种遍历的性质进行了刻画,研究了两种遍历的等价条件.其次,利用Pettis积分、算子值数学期望及广义连续修正模等工具给出广义算子半群的概率逼近表达式.     

渐近殆非扩张曲线的渐近性态及遍历定理

本文在实 Hilbert空间中讨论了渐近殆非扩张曲线的渐近性态及遍历定理 .作为应用 ,给出了非凸闭集上非 Lipschitzian半群的渐近性态及遍历定理     

遍历序列在动力系统平均方法定量研究中的应用

主要研究了遍历序列及其应用.在遍历函数的基础上,引入了遍历序列的概念.然后,从两个方面来研究离散情况下的遍历问题,从中得到了一些遍历序列的性质,并利用平均方法得到了离散情况下的动力系统的解的定量性质.     

一维Brusselator模型

用两种方法证明了一维Brusselator模型对应的Q过程非强遍历.对一个修正的一维Brusse—lator模型,证明了其对应的Q过程是强遍历的.应用其方法研究了一类扩展的分支过程,得到该过程强遍历的一个必要条件.     

随机环境中马氏链的Chacon-Ornstein定理

利用随机环境中马氏链的Hofp极大遍历引理和Brunel极大遍历引理,给出了随机环境中马氏链的Chacon-Ornstein定理和Chacon认证定理.     

Robust Weak Ergodicity And Stable Ergodicity

In this paper, we define robust weak ergodicity and study the relation between robust weak ergodicity and stable ergodicity for conservative partially hyperbolic systems. We prove that a C^r(r > 1) conservative partially hyperbolic diffeomorphism is stably ergodic if it is robustly weakly ergodic and has positive (or negative) central exponents on a positive measure set. Furthermore, if the condition of robust weak ergodicity is replaced by weak ergodicity, then the diffeomophism is an almost stably ergodic system. Additionally, we show in dimension three, a C^r(r > 1) conservative partially hyperbolic diffeomorphism can be approximated by stably ergodic systems if it is robustly weakly ergodic and robustly has non-zero central exponents.     

广义Kolmogorov矩阵的遍历性

在本文中,我们证明了广义Kolmogorov矩阵所对应的Markov链的强遍历性与指数遍历性,并且给出它的最大指数遍历常数的一个下界。     

Ergodicity of a polling network with an infinite number of stations

A Markov polling system with infinitely many stations is studied. The topic is the ergodicity of the infinite-dimensional process of queue lengths. For the infinite-dimensional process, the usual type of ergodicity cannot prevail in general and we introduce a modified concept of ergodicity, namely, weak ergodicity. It means the convergence of finite-dimensional distributions of the process. We give necessary and sufficient conditions for weak ergodicity. Also, the “usual” ergodicity of the system is studied, as well as convergence of functionals which are continuous in some norm. This revised version was published online in June 2006 with corrections to the Cover Date.     

Remark on the Abel Ergodicity of Quasi-pseudo-resolvents

In this note, some results concerning Abel ergodicity of quasi-pseudo-resolvents are obtained.AMS Subject Classification (1991): 47D05.Innovation Project for University Prominent Research Talents of Henan, China     

Ergodicity of Particle Systems

We study shift ergodicity, mixing, and related problems for invariant measures of interacting particle systems. The models we consider here include ferromagnetic stochastic Ising models, voter models, contact processes, exclusion processes, three-opinion noisy biased voter models, multi-opinion voter models, etc. Our results answer some questions for these models. One of the main techniques involved is a duality argument.     

几类遍历性的显式判别准则

关于一维扩散过程或生灭过程的几类遍历性,新近很快地找到了显式判别准则,详见表5．1和5．2,其一是生灭过程的指数遍历性判准,曾是马链的一个长期未解问题,有趣的是,此论题与多个数学分支有关,我们详细介绍后一问题的想法,也建议了若干进一步研究课题。     

一类带随机延滞的时间序列模型的遍历性

本利用马氏化方法和一般状态空间马氏链的基本理论研究了一类带随机延滞的时间序列模型的遍历性，得到了该模型伴随几何遍历的一个判别准则．     

一般状态空间跳过程的强遍历性

研究了一般状态空间跳过程的强遍历性,利用最小非负解理论及马氏性,得到了强遍历性的几个等价条件,把连续时间可数状态马氏链的相关结果推广到一般状态空间跳过程的情形.     

IPP+M/M／C排队的遍历性(英文)

The IP P＋M/M/c queueing system has been extensively used in the modern communication system.The existence and uniqueness of stationary distribution of the queue length L（t）for IP P＋M/M/1 queue has been proved in[10].In this paper,we shall give the su？cient and necessary conditions of l-ergodicity,geometric ergodicity,and prove that they are neither uniformly polynomial ergodicity nor strong ergodicity.     

带随机延滞的ARCH模型的几何遍历性

本文对带随机延滞的ARCH模型进行了分析,并得到该模型伴随几何遍历的一个判别准则.