Fractional interacting particle system: drift parameter estimation via Malliavin calculus
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...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2026 |
| País: | España |
| Institución: | Universitat Pompeu Fabra |
| Repositorio: | Repositorio Digital de la UPF |
| OAI Identifier: | oai:repositori.upf.edu:10230/72173 |
| Acceso en línea: | https://hdl.handle.net/10230/72173 http://dx.doi.org/10.1016/j.spa.2025.104857 |
| Access Level: | acceso abierto |
| Palabra clave: | Fractional Brownian motion Interacting particle system Malliavin calculus Drift parameter estimation McKean-Vlasov equations |
| Sumario: | 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 ->8. 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. |
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