# Hurst index estimation in stochastic differential equations driven by fractional Brownian motion

## TL;DR

This paper develops new estimators for the Hurst index in stochastic differential equations driven by fractional Brownian motion, utilizing Malliavin calculus to analyze quadratic variations and their asymptotic behavior.

## Contribution

It introduces a novel approach to estimate the Hurst index in SDEs driven by fractional Brownian motion using higher order increments and Malliavin calculus techniques.

## Key findings

- Consistent estimators for the Hurst index are constructed.
- Asymptotic properties of the estimators are analyzed.
- Simulation results demonstrate estimator effectiveness.

## Abstract

We consider the problem of Hurst index estimation for solutions of stochastic differential equations driven by an additive fractional Brownian motion. Using techniques of the Malliavin calculus, we analyze the asymptotic behavior of the quadratic variations of the solution, defined via higher order increments. Then we apply our results to construct and study estimators for the Hurst index.