Probabilités
Exponential inequalities for the supremum of some counting processes and their square martingales
Comptes Rendus. Mathématique, Tome 359 (2021) no. 8, pp. 969-982.

Nous établissons ici des inégalités exponentielles pour le supremum de martingales et de martingales carrées issues de processus de comptage, ainsi que pour le processus d’oscillation de ces processus. Ces inégalités, qui jouent un rôle essentiel dans le contrôle d’erreur de certaines procédures statistiques, s’appliquent à des processus de comptage non-explosifs généraux, comme les processus de Poisson, de Hawkes ou encore les processsus de Cox. Quelques applications aux $U$-statistiques sont aussi abordées dans cet article.

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.

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DOI : https://doi.org/10.5802/crmath.206
Classification : 60G55
@article{CRMATH_2021__359_8_969_0,
author = {Ronan Le Gu\'evel},
title = {Exponential inequalities for the supremum of some counting processes and their square martingales},
journal = {Comptes Rendus. Math\'ematique},
pages = {969--982},
publisher = {Acad\'emie des sciences, Paris},
volume = {359},
number = {8},
year = {2021},
doi = {10.5802/crmath.206},
language = {en},
}
Ronan Le Guével. Exponential inequalities for the supremum of some counting processes and their square martingales. Comptes Rendus. Mathématique, Tome 359 (2021) no. 8, pp. 969-982. doi : 10.5802/crmath.206. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.206/

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