Non-Parametric Learning of Stochastic Differential Equations with Non-asymptotic Fast Rates of Convergence
arxiv(2023)
摘要
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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