Hoeffding's inequalities for geometrically ergodic Markov chains on   general state space
  We consider Markov chain with spectral gap in $L^2$ space. Assume that $f$ is a bounded function. Then the probabilities of large deviations of average along trajectory satisfy Hoeffding's-type inequalities. These bounds depend only on the stationary mean, spectral gap and the end-points of support of $f$. 
B{\l}a\.zej Miasojedow
math.PR