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

Abstract

On the basis of results concerning the behavior of the potential of a countable ergodic Markov chain for a certain class of functions, the asymptotic normality of the variable$\tfrac{1}{{\sqrt n }}\sum\nolimits_{k = 0}^{n - 1} {f(X_k )}$ is proved. The asymptotic normality of centered frequencies is obtained without using the condition of finiteness of the timeM ₀τ² of the first return to a chain state.