Central limit theorem for centered frequencies of a countable ergodic markov chain

Abstract

On the basis of results relating to the behavior of the potential of a countable ergodic Markov chain, for a certain class of functions, the asymptotic normality of a variable $\cfrac{1}{\sqrt{n}}\sum^{n-1}_{k=0}f(X_k)$ for $n \rightarrow \infty$ has been proved. The asymptotic normality of the centering frequencies has been obtained without using the finileness conditions for the time $M_0\tau^2$ of the first return into a chain state.