A tail inequality for suprema of unbounded empirical processes with applications to Markov chains

Abstract

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.

The main result in the independent case slightly improved. The presentation changed. To appear in Electronic Journal of Probability

References in corpus (2)

• Concentration around the mean for maxima of empirical processes
• Renewal theory and computable convergence rates for geometrically ergodic Markov chains