一类Feller算子的遍历性质  

On the Ergodic Properties for Class of Feller Operators

作　　者：郭新伟[1] 王焱平[2] 齐海涛[1] 

机构地区：[1]山东大学威海分校数学和统计学院,山东威海264209 [2]上海电力学院数理系,上海200090

出　　处：《南昌大学学报（理科版）》2010年第6期536-540,共5页Journal of Nanchang University(Natural Science)

基　　金：山东省自然科学基金资助项目(ZR2009AQ014)

摘　　要：用分析方法研究紧的度量空间上的一类Feller算子P的遍历性质。通过P的转移概率函数π(·,·),给出了P的极小遍历集的特征。利用Riesz表示定理和平均遍历定理证明了紧的度量空间上具有遍历测度的算子P有几乎稠密的轨道。此外,在P的支集相交这一条件下,得到了算子P具有惟一不变概率测度的充分条件。文中的结论推广和改进了一些已知的结果。The ergodic properties for a class of Feller operators defined on a compact metric space is discussed by using analytic method,and the characteristic of minimal ergodic sets is given by means of the transition function of P.It proves that operator P with a ergodic measure on a compact metric space have almost dense trajectories using Riesz representation theorem and means ergodic theorems.In addition,a sufficient condition of having a unique invariant probability measure is obtained under the condition that P has overlap supports.The conclusions in this paper extend and improve some known results.

关 键 词：FELLER算子 转移概率函数 不变概率测度 遍历性 

分 类 号：O177.99[理学—数学]