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

TL;DR

This paper introduces new strongly consistent and asymptotically normal estimators for the Hurst index in SDEs driven by fractional Brownian motion, using discrete data observations.

Contribution

It proposes novel estimators that are both strongly consistent and asymptotically normal for the Hurst index in fractional SDEs, based on discrete observations.

Findings

Estimators are strongly consistent.

Estimators are asymptotically normal.

Effective for discrete data observations.

Abstract

Strongly consistent and asymptotic normal estimators of the Hurst index of a stochastic differential equation driven by a fractional Brownian motion are proposed. The estimators are based on discrete observations of the underlying process.