  Using the renewal approach we prove exponential inequalities for additive
functionals and empirical processes of ergodic Markov chains, thus obtaining
counterparts of inequalities for sums of independent random variables. The
inequalities do not require functions of the chain to be bounded and moreover
all the involved constants are given by explicit formulas whenever the usual
drift condition holds, which may be of interest in practical applications e.g.
to MCMC algorithms.
