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

作者：Tang Junmin^*; Zhang Jihong; Zhang Xiongying

来源：Acta Mathematica Scientia, 2009, 29(5): 1309-1322.

DOI：10.1016/S0252-9602(09)60105-3

• Markov operator
• invariant measure
• ergodicity
• unidimensionality

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 (Sigma(N)(j=1)p(1j)f(j) o w(1j),..., Sigma(N)(j=1)p(Nj)f(j) o w(Nj))
for any f = (f(1), f(2),..., f(N)), where (p(ij)) is a N x 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.

• 出版日期2009-9
• 单位杭州电子科技大学; 武汉大学; 华南理工大学