Uniform concentration inequality for ergodic diffusion processes observed at discrete times

TL;DR

This paper establishes a concentration inequality for ergodic diffusion processes observed at discrete times, leveraging geometric ergodicity, and applies it to nonparametric drift estimation.

Contribution

It introduces a novel concentration inequality for discrete-time observations of ergodic diffusions, extending theoretical tools for statistical inference.

Findings

Proved a concentration inequality for ergodic diffusions at discrete times.

Applied the inequality to nonparametric drift estimation.

Demonstrated the utility of geometric ergodicity in statistical bounds.

Abstract

In this paper a concentration inequality is proved for the deviation in the ergodic theorem in the case of discrete time observations of diffusion processes. The proof is based on the geometric ergodicity property for diffusion processes. As an application we consider the nonparametric pointwise estimation problem for the drift coefficient under discrete time observations.