# Parametric estimation of stochastic differential equations via online gradient descent

arXiv: https://arxiv.org/abs/2210.08800 · HTML: https://mlsanity.com/paper/2210.08800/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Oct 2022.

## Built on by (most cited first, 1 of 1)

- [Non-Parametric Learning of Stochastic Differential Equations with Non-asymptotic Fast Rates of Convergence](https://mlsanity.com/paper/2305.15557/) (2023)

## Abstract (arXiv)

We propose an online parametric estimation method of stochastic differential equations with discrete observations and misspecified modelling based on online gradient descent. Our study provides uniform upper bounds for the risks of the estimators over a family of stochastic differential equations. The derivation of the bounds involves three underlying theoretical results: the analysis of the stochastic mirror descent algorithm based on dependent and biased subgradients, the simultaneous exponential ergodicity of classes of diffusion processes, and the proposal of loss functions whose approximated stochastic subgradients are dependent only on the known model and observations.