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

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 appro...

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Bibliographic Details
Published in:arXiv.org 2024-12
Main Authors: Bonalli, Riccardo, Alessandro Rudi
Format: Article
Language:English
Subjects:
Differential equations
Drift
Fokker-Planck equation
Learning
Online Access:Get full text
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Summary: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.
ISSN:2331-8422