Séminaire MODAL'X : Chiara Amorino (Universitat Pompeu Fabra, Barcelone)

Publié le 12 septembre 2025 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)

Bâtiment Maurice Allais (G)

Entresol, salle Modal'X (E-27)
Plan d'accès
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