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We take into consideration generalization bounds in [3] 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 nonparametric with respect to the statistical model.We showa practicalway 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.

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Neural Drift Estimation for Ergodic Diffusions: Nonparametric Analysis and Numerical Exploration

  • 会议论文

  • 发表日期：

    2025年

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  • Simone Di Gregorio,
  • Francesco Iafrate

摘要

We take into consideration generalization bounds in [3] 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 nonparametric with respect to the statistical model.We showa practicalway 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.