# A general drift estimation procedure for stochastic differential equations with additive fractional noise

## TL;DR

This paper introduces a general method for estimating the drift in stochastic differential equations driven by additive fractional Brownian motion, utilizing invariant measure identification under ergodic conditions, with proven consistency and convergence insights.

## Contribution

It presents a novel drift estimation procedure for SDEs with fractional noise based on invariant measure identification, including consistency and convergence analysis.

## Key findings

- The estimation method is consistent under ergodic assumptions.
- Examples provided where the invariant measure is identifiable.
- Convergence rates are discussed for the proposed estimator.

## Abstract

In this paper we consider the drift estimation problem for a general differential equation driven by an additive multidimensional fractional Brownian motion, under ergodic assumptions on the drift coefficient. Our estimation procedure is based on the identification of the invariant measure, and we provide consistency results as well as some information about the convergence rate. We also give some examples of coefficients for which the identifiability assumption for the invariant measure is satisfied.