# Concentration inequalities for Stochastic Differential Equations with additive fractional noise

## TL;DR

This paper develops concentration inequalities for solutions of additive stochastic differential equations driven by fractional Brownian motion, applicable to both continuous and discrete observations, with applications to occupation measures.

## Contribution

It introduces new concentration inequalities for SDEs with fractional noise, extending existing results to fractional Brownian motion-driven systems.

## Key findings

- Established concentration bounds for functionals of SDE solutions with fractional noise
- Derived inequalities for discrete-time observations of the process
- Applied results to occupation measures of the process

## Abstract

In this paper, we establish concentration inequalities both for functionals of the whole solution on an interval [0, T ] of an additive SDE driven by a fractional Brownian motion with Hurst parameter H $\in$ (0, 1) and for functionals of discrete-time observations of this process. Then, we apply this general result to specific functionals related to discrete and continuous-time occupation measures of the process.