IS01: Statistics for Stochastic Processes

Organizer: Fabienne Comte (Université Paris Cité, MAP5)

Fractional interacting particle system: drift parameter estimation via Malliavin calculus

Chiara Amorino

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.

This is based on a joint work with I. Nourdin and R. Shevchenko.