Exponential inequalities for the supremum of some counting processes and their square martingales

Ronan Le Guével (1, 2)

1 UR2 - Université de Rennes 2
2 IRMAR - Institut de Recherche Mathématique de Rennes

We establish exponential inequalities for the supremum of martingales and square martingales obtained from counting processes, as well as for the oscillation modulus of these processes. Our inequalities, that play a decisive role in the control of errors in statistical procedures, apply to general non-explosive counting processes including Poisson, Hawkes and Cox models. Some applications for $U$-statistics are discussed.

Mots clés: U-statistics; exponential martingales; concentration inequalities; Counting processes

Domaines: Probabilités [math.PR]

Ronan Le Guével. Exponential inequalities for the supremum of some counting processes and their square martingales. 2020. ⟨hal-02275583v3⟩