Work

Non-parametric Learning of Stochastic Differential Equations with Non-asymptotic Fast Rates of Convergence

Year: 2025

Type: article

Abstract: We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of multi-dimensional non-linear stochastic differential equations, which relies upon discrete-time 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 non-asymptotic 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 be profitably leveraged to enable efficient numerical implementation, offering excellent balance between precision and computational complexity.

Source: Foundations of Computational Mathematics

DOI: 10.1007/s10208-025-09705-x

Authors: Riccardo Bonalli, Alessandro Rudi