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

arXiv: https://arxiv.org/abs/2505.24383 · HTML: https://mlsanity.com/paper/2505.24383/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 10 references that are in the map.
- First posted on arXiv 30 May 2025.

## Builds on (most cited first, 2 of 2)

- [Deep Neural Network Approximation Theory](https://mlsanity.com/paper/1901.02220/) (2019)
- [Statistical Guarantees for Regularized Neural Networks](https://mlsanity.com/paper/2006.00294/) (2020)

## Abstract (arXiv)

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 Ito-Taylor approximation of the sample paths.