Acta mathematica scientia, Series B >
UNIQUENESS, ERGODICITY AND UNIDIMENSIONALITY OF INVARIANT MEASURES UNDER A MARKOV OPERATOR
Received date: 2007-01-28
Online published: 2009-09-20
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 fj ο 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
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 . DOI: 10.1016/S0252-9602(09)60105-3
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