Nonparametric Estimation of the Diffusion-Interaction Function in Particle Systems
Abstract
We study the problem of nonparametric estimation of the interaction function in particle systems whose interaction enters through the diffusion coefficient. The particle system is observed discretely over a fixed time interval, and the interaction function is assumed to belong to a suitable nonparametric function class. We propose an estimation procedure based on empirical risk minimization over finite-dimensional sieve spaces, introducing a computable contrast function that exploits the local volatility of the observed trajectories. We derive a general non-asymptotic error bound under the intrinsic norm associated with the statistical problem and, focusing the analysis on multiresolution wavelet approximation spaces, we obtain explicit polynomial convergence rates in two distinct regimes, depending on whether the particle or discretization error dominates. Finally, we establish convergence rates for the classical L2-norm.
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BibTeX
@misc{amorino2026nonparametric,
title = {{Nonparametric Estimation of the Diffusion-Interaction Function in Particle Systems}},
author = {Chiara Amorino and Francisco Pina and Mark Podolskij},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24374},
eprint = {2609.24374},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24374},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Nonparametric Estimation of the Diffusion-Interaction Function in Particle Systems
AU - Chiara Amorino
AU - Francisco Pina
AU - Mark Podolskij
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24374
UR - https://arxiv.org/abs/2609.24374
AB - We study the problem of nonparametric estimation of the interaction function in particle systems whose interaction enters through the diffusion coefficient. The particle system is observed discretely over a fixed time interval, and the interaction function is assumed to belong to a suitable nonparametric function class. We propose an estimation procedure based on empirical risk minimization over finite-dimensional sieve spaces, introducing a computable contrast function that exploits the local volatility of the observed trajectories. We derive a general non-asymptotic error bound under the intrinsic norm associated with the statistical problem and, focusing the analysis on multiresolution wavelet approximation spaces, we obtain explicit polynomial convergence rates in two distinct regimes, depending on whether the particle or discretization error dominates. Finally, we establish convergence rates for the classical L^2-norm.
ER -