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

doi:10.1016/S0252-9602(09)60105-3

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

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

唐军民, 张继宏, 章雄鹰

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.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/Abstract

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=1^Np_1jf_j ο w_1j, …, ∑_j=1^Np_Njf_jο w_Nj)
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:

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

中图分类号:

37A30

唐军民, 张继宏, 章雄鹰. UNIQUENESS, ERGODICITY AND UNIDIMENSIONALITY OF INVARIANT MEASURES UNDER A MARKOV OPERATOR[J]. 数学物理学报(英文版), 2009, 29(5): 1309-1322.

TANG Jun-Min, ZHANG Ji-Hong, ZHANG Xiong-Ying. UNIQUENESS, ERGODICITY AND UNIDIMENSIONALITY OF INVARIANT MEASURES UNDER A MARKOV OPERATOR[J]. Acta mathematica scientia,Series B, 2009, 29(5): 1309-1322.

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

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

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