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Preprints, Working Papers, ... Year : 2024

EXPONENTIAL INEQUALITIES FOR SUPREMA OF PROCESSES WITH STOCHASTIC NORMALIZATION

Abstract

We prove a deviation bound for the supremum of a normalized process derived from a real-valued random process $(Y_t)_{t \in S}$. Assuming the increments $Y_t - Y_s$ satisfy Bernstein deviation bounds with random fluctuation terms makes it possible to use a stochastic normalization term. This improves on classical versions where the control of the fluctuation is deterministic.
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hal-04526484 , version 1 (29-03-2024)

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  • HAL Id : hal-04526484 , version 1

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Julien Aubert, Luc Lehéricy. EXPONENTIAL INEQUALITIES FOR SUPREMA OF PROCESSES WITH STOCHASTIC NORMALIZATION. 2024. ⟨hal-04526484⟩
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