Neural Drift Estimation for Ergodic Diffusions: Non-parametric Analysis and Numerical Exploration
Statistics Theory
2025-06-02 v1 Machine Learning
Statistics Theory
Abstract
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 It\^o-Taylor approximation of the sample paths.
Keywords
Cite
@article{arxiv.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}
}