On some estimators of the Hurst index of the solution of SDE driven by a fractional Brownian motion

TL;DR

This paper proposes strongly consistent and asymptotically normal estimators for the Hurst parameter of solutions to SDEs driven by fractional Brownian motion, using discrete observations of the processes.

Contribution

It introduces new estimators for the Hurst parameter that are proven to be strongly consistent and asymptotically normal, based on discrete data.

Findings

Estimators are strongly consistent.

Estimators are asymptotically normal.

Effective with discrete observations.

Abstract

Strongly consistent and asymptotically normal estimators of the Hurst parameter of solutions of stochastic differential equations are proposed. The estimators are based on discrete observations of the underlying processes.