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

• URL: http://arxiv.org/abs/2305.15557v2
• Date: Tue, 23 Apr 2024 11:34:52 GMT
• Title: Non-Parametric Learning of Stochastic Differential Equations with Non-asymptotic Fast Rates of Convergence
• Authors: Riccardo Bonalli, Alessandro Rudi,
• Abstract summary: We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of non-linear differential equations. The key idea essentially consists of fitting a RKHS-based approximation of the corresponding Fokker-Planck equation to such observations.
• Score: 65.63201894457404
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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