摘要：For an irreducible Markov chain $(X_n)_{n\ge 0}$ we identify the rate function governing the large deviation estimation of empirical mean $\frac ){n} \sum_{k=0}^{n-1} f(X_k)$ by means of the Donsker-Varadhan's entropy. That allows us to obtain the lower bound of large deviations for the empirical measure $\frac ){n} \sum_{k=0}^{n-1} \delta_{X_k}$ in full generality
