2025/02/10 by Chiara Amorino, Amorino, Chiara, Ivan Nourdin +3 · 1 citation
Physics and Astronomy · Materials Science · #Advanced Thermodynamics and Statistical Mechanics #Spectroscopy and Quantum Chemical Studies #Material Dynamics and Properties
paper · pdf · doi:10.48550/arxiv.2502.06514
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 \( H ≥ 1/2 \). Considering continuous observation of the interacting particles over a fixed interval \([0, T]\), we examine the asymptotic regime as \( N → ∞ \). 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 \( H ∈ (0,1) \). 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.