Article Dans Une Revue Foundations of Computational Mathematics Année : 2025

Non-Parametric Learning of Stochastic Differential Equations with Fast Rates of Convergence

Résumé

We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of non-linear stochastic differential equations, which relies upon discretetime observations of the state. The key idea essentially consists of fitting a RKHS-based approximation of the corresponding Fokker-Planck equation to such observations, yielding theoretical estimates of learning rates which, unlike previous works, become increasingly tighter when the regularity of the unknown drift and diffusion coefficients becomes higher. Our method being kernel-based, offline pre-processing may in principle be profitably leveraged to enable efficient numerical implementation.

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hal-04381810 , version 1 (09-01-2024)
hal-04381810 , version 2 (15-02-2025)
hal-04381810 , version 3 (28-02-2025)
hal-04381810 , version 4 (07-03-2025)

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Riccardo Bonalli, Alessandro Rudi. Non-Parametric Learning of Stochastic Differential Equations with Fast Rates of Convergence. Foundations of Computational Mathematics, 2025. ⟨hal-04381810v4⟩
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