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Séminaire MODAL'X : Chiara Amorino (Universitat Pompeu Fabra, Barcelone)
Publié le 12 septembre 2025
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Mis à jour le 22 septembre 2025
Fractional interacting particle system: drift parameter estimation via Malliavin calculus
Date(s)
le 25 septembre 2025
13h30 - 14h30
Lieu(x)
Résumé : We address the problem of estimating the drift parameter in a system of $N$ interacting particles driven by additive fractional Brownian motion of Hurst index \( H \geq 1/2 \). Considering continuous observation of the interacting particles over a fixed interval \([0, T]\), we examine the asymptotic regime as \( N \to \infty \). Our main tool is a random variable reminiscent of the least squares estimator but unobservable due to its reliance on the Skorohod integral. We demonstrate that this object is consistent and asymptotically normal by establishing a quantitative propagation of chaos for Malliavin derivatives, which holds for any \( H \in (0,1) \). Leveraging a connection between the divergence integral and the Young integral, we construct computable estimators of the drift parameter. These estimators are shown to be consistent and asymptotically Gaussian. Finally, a numerical study highlights the strong performance of the proposed estimators.
Mis à jour le 22 septembre 2025