# Sparse inference of the drift of a high-dimensional Ornstein-Uhlenbeck process

arXiv: https://arxiv.org/abs/1707.03010 · HTML: https://mlsanity.com/paper/1707.03010/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jul 2017.

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

- [Concentration analysis of multivariate elliptic diffusion processes](https://mlsanity.com/paper/2206.03329/) (2022)

## Abstract (arXiv)

Given the observation of a high-dimensional Ornstein-Uhlenbeck (OU) process in continuous time, we proceed to the inference of the drift parameter under a row-sparsity assumption. Towards that aim, we consider the negative log-likelihood of the process, penalized by an ℓ1-penalization (Lasso and Adaptive Lasso). We provide both non-asymptotic and asymptotic results for this procedure, by means of a sharp oracle inequality, and a limit theorem in the long-time asymptotics, including asymptotic consistency for variable selection. As a by-product, we point out the fact that for the Ornstein-Uhlenbeck process, one does not need an assumption of restricted eigenvalue type in order to derive fast rates for the Lasso, while it is well-known to be mandatory for linear regression for instance. Numerical results illustrate the benefits of this penalized procedure compared to standard maximum likelihood approaches both on simulations and real-world financial data.