两类无穷质点马氏过程的可逆性

本文讨论了广义自旋变相过程和广义排它过程的可逆性,文中应用[4]的抽象场论的方法,给出了这两类过程的有势性判别准则,对广义自旋证明了有势等价于可逆,在有势的条件下可逆测度可由速度函数构造的Gibbs态刻划。对广义排它则证明了可逆测度必然存在,若可正逆测度存在则它有势,且在有势的条件下,可逆测度也可由速度函数构造的Gibbs态刻划,     

AN ERGODIC THEOREM FOR GENERALIZED SIMPLE EXCLUSION PROCESSES WITH REVERSIBLE POSITIVE TRANSITION

Simple exclusion procosses are important infinite particle systems. This model was proposed by Spitzer (1)and studied extensively by Spitzer and Liggett (2). On the basis of the model, Yan Shi-jian and Chen Mu-fa proposed generalized exclusion processes and obtained the construction of the processes. Zheng Wen-qu obtained a necessary and sufficient condition of the reversibility and proved that the set of the reversible probability measures of such a process is equal to the set of it's Gibbs states (3). This paper is devoted to the ergodic theory of a generalized simple exclusion proess with the state space {0, 1, …, m} (m≥1, S is a countable set) and a reversible positive recurrent transition probability matrix P=(p(x, y))_(x,y)∈s Refering (4), the set of it's invariant probability measures is described and the ergodic properties of the process is obtained. We also prove that the set of it's reversible probability measures coinsides with the set of it's invariant probability measures. So the main re     

《分形几何——数学基础及其应用》评介

分形几何做为一门新兴的数学分支已显示它的深刻的理论内涵及广泛的应用前景。目前,国内外已出现了有关分形的许多专著,除了Mandelbrot B.的几部经典著作外,英国数学家Falconer K.1985年出版的“The Geometry of Fractal Sets”(《分形集几何》)是公认的有关分形数学理论方面的权威著作。但该书起点较高,贯穿全书的几何测度论使许多人望而却步,它只适宜有较深数学素养的人阅读。     

具有有势平移不变迁移的广义简单排它过程

§1 引言自从Spitzer 1970年提出简单排它过程的概率模型以来,Liggett和Spitzer在七十年代初对它做了大量的工作。在迁移概率对称或平移不变或可逆正常返的条件下,他们基本解决了过程的遍历性。最近Arratia又研究了该过程中带有标记的质点的极限定理。作者在[10]     

稳定随机游动重点集的离散豪斯道夫维数

设是ｄ维格子点上的严格α－稳定的随机游动，称为的Ｐ重点集（Ｐ１），本文讨论了的离散豪斯道夫维数，并对，（ａ＜ｄ），证明了Ｐ重点集的维数都等于ａ，即     

广义谢尔宾斯基海绵的Packing测度

讨论了三维欧氏空间上的一类自仿射集──广义谢尔宾斯基(Sierpinski)海绵的填充测度(Packing Measure),对φ(t)=t^θ,φ(t)=t^θ/|logt|及更一般的情况,证明了填充测度P_ψ[K(T,D)]为无穷或有限的条件,