Non-Parametric Learning of Stochastic Differential Equations with Fast
  Rates of Convergence
Riccardo Bonalli Alessandro Rudi
We propose a novel non-parametric learning paradigm for the identification of
drift and diffusion coefficients of 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 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 in
principle be profitably leveraged to enable efficient numerical implementation.