Hoeffding's inequality for supermartingales

Xiequan Fan (1) , Ion Grama (1) , Quansheng Liu (1)

1 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

We give an extension of Hoeffding's inequality to the case of supermartingales with differences bounded from above. Our inequality strengthens or extends the inequalities of Freedman, Bernstein, Prohorov, Bennett and Nagaev.

Mots clés: Concentration inequalities; Hoeffding's inequality; Freedman's inequality; Bennett's inequality; martingales; supermartingales

Domaines: Probabilités [math.PR]

Xiequan Fan, Ion Grama, Quansheng Liu. Hoeffding's inequality for supermartingales. Stochastic Processes and their Applications, 2012, 122, pp.3545-3559. ⟨hal-00905536v2⟩