数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (5): 1309-1322.doi: 10.1016/S0252-9602(09)60105-3

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UNIQUENESS, ERGODICITY AND UNIDIMENSIONALITY OF INVARIANT MEASURES UNDER A MARKOV OPERATOR

 唐军民, 张继宏, 章雄鹰   

  1. 1.School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
    2.Institute of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, China
    3.Department of Mathematics, South China University of Technology, Guangzhou 510640, China
  • 收稿日期:2007-01-28 出版日期:2009-09-20 发布日期:2009-09-20

UNIQUENESS, ERGODICITY AND UNIDIMENSIONALITY OF INVARIANT MEASURES UNDER A MARKOV OPERATOR

 TANG Jun-Min, ZHANG Ji-Hong, ZHANG Xiong-Ying   

  1. 1.School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
    2.Institute of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, China
    3.Department of Mathematics, South China University of Technology, Guangzhou 510640, China
  • Received:2007-01-28 Online:2009-09-20 Published:2009-09-20

摘要:

Let X be a compact metric space and C(X) be the space of all continuous functions on X. In this article, the authors
consider the Markov operator T:C(X)N → C(X)N defined by
Tf = (∑j=1Np1j fj ο w1j, …, ∑j=1N pNj fο wNj)
for any f =(f 1, f 2, …, f N), where (p ij) is a N × N transition probability matrix and {w ij} is an family of continuous transformations on X. The authors study the uniqueness, ergodicity and unidimensionality of T*-invariant measures where T* is the adjoint operator of T.

关键词: Markov operator, invariant measure, ergodicity, unidimensionality

Abstract:

Let X be a compact metric space and C(X) be the space of all continuous functions on X. In this article, the authors
consider the Markov operator T:C(X)N → C(X)N defined by
Tf = (∑j=1Np1j fj ο w1j, …, ∑j=1N pNj fο wNj)
for any f =(f 1, f 2, …, f N), where (p ij) is a N × N transition probability matrix and {w ij} is an family of continuous transformations on X. The authors study the uniqueness, ergodicity and unidimensionality of T*-invariant measures where T* is the adjoint operator of T.

Key words: Markov operator, invariant measure, ergodicity, unidimensionality

中图分类号: 

  • 37A30