Self-normalized Cramér-type Moderate Deviations for Functionals of Markov Chain

Let x n , n ≥ 0} be a Markov chain with a countable state space S and let f (·) be a measurable function from S to ℝ and consider the functionals of the Markov chain y n := f ( x n ). We construct a new type of self-normalized sums based on the random-block scheme and establish a Cramér-type moderate deviations for self-normalized sums of functionals of the Markov chain.