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

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

Abstract

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=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.

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

CLC Number:

37A30

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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