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Fractional interacting particle system: Drift parameter estimation via Malliavin calculus

Author

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  • Amorino, Chiara
  • Nourdin, Ivan
  • Shevchenko, Radomyra

Abstract

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.

Suggested Citation

  • Amorino, Chiara & Nourdin, Ivan & Shevchenko, Radomyra, 2026. "Fractional interacting particle system: Drift parameter estimation via Malliavin calculus," Stochastic Processes and their Applications, Elsevier, vol. 195(C).
    • Handle: RePEc:eee:spapps:v:195:y:2026:i:c:s0304414925003011
    DOI: 10.1016/j.spa.2025.104857
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