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

Abstract : 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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https://hal.archives-ouvertes.fr/hal-02275583
Contributor : Ronan Le Guével <>
Submitted on : Saturday, December 12, 2020 - 2:34:23 PM
Last modification on : Friday, January 8, 2021 - 3:39:57 AM

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  • HAL Id : hal-02275583, version 3

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

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