Chernoff and Berry-Esséen inequalities for Markov Processes

Pascal Lezaud (1)

1 DGAC - Direction Générale de l'Aviation Civile

In this paper, we develop bounds on the distribution function of the empirical mean for general ergodic Markov processes having a spectral gap. Our approach is based on the perturbation theory for linear operators, following the technique introduced by Gillman.

Mots clés: Markov process; Chernoff bound; Berry-Esséen; eigenvalues; perturbation theory

Domaines: Mathématiques [math]; Probabilités [math.PR]

Pascal Lezaud. Chernoff and Berry-Esséen inequalities for Markov Processes. ESAIM: Probability and Statistics, 2001, 5, pp 183-201. ⟨10.1051/ps:2001108⟩. ⟨hal-00940906⟩