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本文利用构造鞅的方法, 研究了Cayley树图上奇偶马氏链场的强极限定理, 给出了Cayley树图上奇偶马氏链场关于状态和状态序偶出现频率的强大数定律, 推广了一个已知结果.     

正规Cayley图

综述了自１９９０年以来１２－传递图研究的一些新成果,正规Ｃａｙｌｅｙ图的相关结论。     

Cayley定理及其证明

<正>Cayley定理简介对于欧氏平面上的三角形及其相关的全等问题,以及由三角形已知的边和角利用正弦定理和余弦定理求解三角形等问题,中学生一般都很熟悉.对于平面四边形,除了特殊的如梯形、平行四边形或者更特殊的菱形、长方形等以外,大家对它们的性质了解得还不多.比如Cayley定理,很多中学生都不了解.Cayley定理断言,四边形的四条边和两条对角线满足一个代数关系,即存在一个六元多项式F,使得对于任意四边形ABCD,有     

一类非正规Cayley有向图

本文研究了2p2(p奇素数)阶非交换群上两度Cayley有向图的正规性,发现 了一无限族非正规的Cayley有向图.     

Cayley定理的一个应用

在平面几何里,众所熟知,有一个联系着三角形面积,外接圆半径和三边乘积的公式:     

pqr阶Cayley图是Hamilt

本文证明了pqr阶连通的Cayley图是Hamilton图,这里p,q,r为相异素数.     

极小Cayley图的限制性边连通度

一个连通图X的边集的一个子集C称为一个限制性边割,如果它是一个边割,且X／C不含孤立点。X的限制性边连通度λ′（X）定义为所有限制性边割的最小基数。本文完全决定了极小Cayley图的限制性边连通度。     

一类新的交错群Cayley网络

本文利用交错群的Ｃａｙｌｅｙ图构作了一类互连网络,进而讨论了它的直径,容错度,容错直径和Ｈａｍｉｌｔｏｎ连通性,这些性质表明它优于利用交错群构作的网络ＡＧｎ,且相似于著名的星形网络。     

有限群的正规Cayley图

证明了每个有限群G有正规Cayley图除非G~₌Z₄×Z₂ 或G~₌Q₈×Z^r₂ (r≥0 ) ;每个有限群都有正规Cayley有向图 ,其中Z_m 表示m阶循环群,Q₈表示8阶四元数群.     

完全正则半群的Cayley表示

本文利用点集映射和等价关系得出了完全正则半群的Ｃａｙｌｅｙ表示，从而解决了１９８７年Ｍ．Ｐｅｔｒｉｃｈ提出的一个公开问题．作为特例，还得到完全单半群的ｃａｙｌｅｙ表示．     

Cayley树上非对称马氏链的强大数定律及渐近均分割性

In this paper,we study the strong law of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain（NSMC） indexed by Cayley tree with any finite states.The asymptotic equipartition properties with almost everywhere（a.e.） convergence for NSMC indexed by Cayley tree are obtained.This article generalizes a recent result.     

Asymptotic Energy Equipartition for the Wave Equation on Homogeneous Trees

 Let ? be a homogeneous tree, ℒbe the Laplace operator of ?, and b be the bottom of its L ² spectrum. Let u be a solution of the (modified) wave equation on ?. Using Fourier analysis on ? we show that the energy of u is asymptotically divided into equal potential and kinetic parts. Received 13 January 1997; in final form 23 March 1998     

Asymptotic inference for continuous-time Markov chains

Summary This paper deals with asymptotic optimal inference in a time-continuous ergodic Markov chain with countable state space, based on observation of the process up to timet. Let the infinitesimal generator depend on an unknown parameter. Under weak assumptions on the parametrization, we show local asymptotic normality for the statistical model ast. As a consequence, limit distributions of sequences of competing estimators for the unknown parameter are more spread out than a specified normal distribution.     

Bethe树和Cayley树上奇偶马尔可夫链场的强极限定理

本文介绍了N元Bethe树TB,N(N元Cayley树TC,N)上的奇偶马尔可夫链场的定义,并通过构造两个非负鞅证得了随机变量序列的强极限定理,应用此强极限定理获得了奇偶马尔可夫链场上的一个强极限定理,作为它的推论得到了状态和状态序偶出现频率的一类强极限定理及其估计,从而推广了关于N元Bethe树上马氏链场和二进树上奇偶马氏链场的部分强极限定理.     

Asymptotic expansions for Laplace transforms of Markov processes

Let ${\mu }^{?}$ be the probability measures on $D[0,T]$ of suitable Markov processes ${\{{\xi }_t^{?}\}}_{0\le t\le T}$ (possibly with small jumps) depending on a small parameter $?>0$, where $D[0,T]$ denotes the space of all functions on $[0,T]$ which are right continuous with left limits. In this paper we investigate asymptotic expansions for the Laplace transforms ${\int }_{D[0,T]}\exp ?\{{?}^{?1}F(x)\}{\mu }^{?}(dx)$ as $?\to 0$ for smooth functionals F on $D[0,T]$. This study not only recovers several well-known results, but more importantly provides new expansions for jump Markov processes. Besides several standard tools such as exponential change of measures and Taylor's expansions, the novelty of the proof is to implement the expectation asymptotic expansions on normal deviations which were recently derived in [13].     

Asymptotic separation for independent trajectories of Markov processes

We say that n independent trajectories ξ₁(t),…,ξ _n (t) of a stochastic process ξ(t)on a metric space are asymptotically separated if, for some ɛ > 0, the distance between ξ _i (t _i ) and ξ _j (t _j ) is at least ɛ, for some indices i, j and for all large enough t ₁,…,t _n , with probability 1. We prove sufficient conitions for asymptotic separationin terms of the Green function and the transition function, for a wide class of Markov processes. In particular,if ξ is the diffusion on a Riemannian manifold generated by the Laplace operator Δ, and the heat kernel p(t, x, y) satisfies the inequality p(t, x, x) ≤ Ct ^−ν/2 then n trajectories of ξ are asymptotically separated provided . Moreover, if for some α∈(0, 2)then n trajectories of ξ^(α) are asymptotically separated, where ξ^(α) is the α-process generated by −(−Δ)^α/2. Received: 10 June 1999 / Revised version: 20 April 2000 / Published online: 14 December 2000 RID="*" ID="*" Supported by the EPSRC Research Fellowship B/94/AF/1782 RID="**" ID="**" Partially supported by the EPSRC Visiting Fellowship GR/M61573     

A Markov Property for Set-Indexed Processes

We consider a type of Markov property for set-indexed processes which is satisfied by all processes with independent increments and which allows us to introduce a transition system theory leading to the construction of the process. A set-indexed generator is defined such that it completely characterizes the distribution of the process.     

二进树上奇偶马氏链场的若干强极限定理与Shannon-McMillan定理的一种逼近

本文建立了二进树上奇偶马氏链场关于状态和状态序偶出现频率的若干强极限定理，其中包括渐近熵密度上、下界的一个估计式及Shannon-McMillan定理的一种逼近。证明中将研究马氏链强极限定理的一种新的分析方法推广到马氏链场的情况。