Ergodicity and central limit theorems for a class of Markov processes (Q1111244)

The paper looks at the following class of discrete parameter Markov processes that take values in an arbitrary complete separable metric space S: \(X_ n=\alpha_ n\alpha_{n-1}...\alpha_ 1X_ 0\) where \(\{\alpha_ n\}\) are independent identically distributed random maps on S into S; \(X_ 0\) is a random variable with values in S and independent of the sequence \(\{\alpha_ n\}.\) An ergodic theorem for \(\{X_ n\}\) and a functional central limit theorem for \(\{f(X_ n)\}\) are proved.