On the number of crossings and bouncings of a diffusion at a sticky threshold - Probabilités et statistiques
Pré-Publication, Document De Travail Année : 2024

On the number of crossings and bouncings of a diffusion at a sticky threshold

Résumé

We distinguish between three types of crossing of a sticky threshold by a onedimensional diffusion. We examine the limit behavior of the corresponding number of crossings statistics and prove that each of these statistics has a different asymptotic regime. We define the notions of bouncing as the symmetric counterparts of crossings. We prove similar results for the number of bouncings at reflecting and non-reflecting sticky thresholds. Using these, we develop consistent stickiness parameter estimators for sticky diffusions and sticky-reflecting Brownian motion.

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hal-04755893 , version 1 (28-10-2024)

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  • HAL Id : hal-04755893 , version 1

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Sara Mazzonetto, Alexis Anagnostakis. On the number of crossings and bouncings of a diffusion at a sticky threshold. 2024. ⟨hal-04755893⟩
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