The number of crossings statistics in local time estimation for Sticky-threshold diffusions

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• Sara Mazzonetto (Université de Lorraine)
• Tuesday 06 August 2024, 14:00-15:00
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SSDW02 - Stochastic reflection

The renormalized number of crossings statistics is known to be a local time estimator of the local time for Brownian motion whose trajectory is observed in high-frequency. Instead of Brownian motion, we consider some one-dimensional diffusions whose behavior is perturbed by the presence of a barrier-point. The perturbation nature, that is partial-reflection (skew BM) or stickiness, is encoded by parameters.In the case of skew BM, the number of crossings is renormalized (as for BM) and it converges towards the local time with a non standard rate of 1/4. It follows asymptotically a a mixed normal law. In case of sticky behavior these results do not hold anymore, different scalings rise up according to the definition of crossings.This talk is partially based on joint works with A. Anagnostakis (LJK Grenoble).

This talk is part of the Isaac Newton Institute Seminar Series series.

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