Neural Drift Estimation for Ergodic Diffusions: Non-parametric Analysis and Numerical Exploration

We take into consideration generalization bounds for the problem of the estimation of the drift component for ergodic stochastic differential equations, when the estimator is a ReLU neural network and the estimation is non-parametric with respect to the statistical model. We show a practical way to enforce the theoretical estimation procedure, enabling inference on noisy and rough functional data. Results are shown for a simulated Itô-Taylor approximation of the sample paths.

@article{gregorio2025_2505.24383,
  title={ Neural Drift Estimation for Ergodic Diffusions: Non-parametric Analysis and Numerical Exploration },
  author={ Simone Di Gregorio and Francesco Iafrate },
  journal={arXiv preprint arXiv:2505.24383},
  year={ 2025 }
}