Parametric estimation of stochastic differential equations via online gradient descent
Statistics Theory
2022-10-18 v1 Optimization and Control
Probability
Statistics Theory
Abstract
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.
Cite
@article{arxiv.2210.08800,
title = {Parametric estimation of stochastic differential equations via online gradient descent},
author = {Shogo Nakakita},
journal= {arXiv preprint arXiv:2210.08800},
year = {2022}
}