Non-parametric Learning of Stochastic Differential Equations with Non-asymptotic Fast Rates of Convergence.
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| Title: | Non-parametric Learning of Stochastic Differential Equations with Non-asymptotic Fast Rates of Convergence. |
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| Authors: | Bonalli, Riccardo1 (AUTHOR) riccardo.bonalli@cnrs.fr, Rudi, Alessandro2 (AUTHOR) alessandro.rudi@sdabocconi.it |
| Source: | Foundations of Computational Mathematics. Jun2026, Vol. 26 Issue 3, p1497-1552. 56p. |
| Subjects: | Stochastic differential equations, Nonparametric estimation, Reproducing kernel (Mathematics), Numerical analysis, Fokker-Planck equation, Drift diffusion models, Kernel functions |
| 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. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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| 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. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 16153375 |
| DOI: | 10.1007/s10208-025-09705-x |
