We present a tail inequality for suprema of empirical processes generated by variables with finite $\psi_\alpha$ norms and apply it to some geometrically ergodic Markov chains to derive similar estimates for empirical processes of such chains, generated by bounded functions. We also obtain a bounded difference inequality for symmetric statistics of such Markov chains.
"A tail inequality for suprema of unbounded empirical processes with applications to Markov chains." Electron. J. Probab. 13 1000 - 1034, 2008. https://doi.org/10.1214/EJP.v13-521