Minimax rates of convergence for the nonparametric estimation of the diffusion coefficient from time-homogeneous SDE paths

Eddy-Michel Ella-Mintsa ()
Additional contact information
Eddy-Michel Ella-Mintsa: Université Gustave Eiffel

Statistical Inference for Stochastic Processes, 2025, vol. 28, issue 3, No 5, 49 pages

Abstract: Abstract Consider a diffusion process $$X = (X_t)_{t \in [0,T]}, ~ T > 0$$ X = ( X t ) t ∈ [ 0 , T ] , T > 0 , solution of a time-homogeneous stochastic differential equation observed at discrete times and high frequency. We assume that the drift and diffusion coefficients of the process X are unknown. In this paper, we study the minimax convergence rates of projection estimators of the square of the diffusion coefficient. Two observation schemes are considered depending on the estimation interval. The square of the diffusion coefficient is estimated on the real line from repeated observations of the process X, where the number of diffusion paths tends to infinity. For the case of a compact estimation interval, we study projection estimators of the square of the diffusion coefficient constructed from a single diffusion path on one side and from repeated observations on the other side, where the number of trajectories tends to infinity. In each of these cases, we establish minimax convergence rates of the worst risk of estimation over a space of Hölder functions.

Keywords: Nonparametric estimation; Diffusion process; Diffusion coefficient; Least squares contrast; Minimax rates; 62G05; 62M05; 60J60 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11203-025-09335-8 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sistpr:v:28:y:2025:i:3:d:10.1007_s11203-025-09335-8

Ordering information: This journal article can be ordered from
http://www.springer. ... ty/journal/11203/PS2

DOI: 10.1007/s11203-025-09335-8

Access Statistics for this article

Statistical Inference for Stochastic Processes is currently edited by Denis Bosq, Yury A. Kutoyants and Marc Hallin

More articles in Statistical Inference for Stochastic Processes from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().