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

arXiv:2305.15557v2 Announce Type: replace
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 …

abstract approximation arxiv convergence cs.lg cs.sy differential diffusion drift eess.sy identification key linear math.oc non-linear non-parametric novel paradigm parametric state stochastic the key type