Moderate deviation principle for exponentially ergodic Markov chain

B. Delyon, A. Juditsky, R. Liptser

For $1/2<\alpha <1$, we propose the MDP analysis for family $$S_n^{\alpha }=\frac{1}{n^{\alpha }}\sum _{i=1}^{n}H(X_{i-1}),n\ge 1,$$ where $(X_n{)}_{n\ge 0}$ be a homogeneous ergodic Markov chain, $X_n\…